// Numbas version: exam_results_page_options
{"name": "Indices", "feedback": {"allowrevealanswer": true, "showtotalmark": true, "advicethreshold": 0, "intro": "", "feedbackmessages": [], "showanswerstate": true, "showactualmark": true}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "metadata": {"description": "<p>Rules of indices, simplifying indices, equations involving indices</p>\n<p>rebelmaths</p>\n<p></p>", "licence": "None specified"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Q1 Indices in their simplest form 1", "extensions": [], "custom_part_types": [], "resources": [["question-resources/5041109_orig.png", "/srv/numbas/media/question-resources/5041109_orig.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num11", "num12", "ans11a", "ans12a", "ans13a", "ans14a", "ans11", "ans12", "ans13", "ans14", "num21", "num22", "ans21", "ans22", "num23", "ans23a", "ans23b", "ans23c", "ans24a", "num24a", "ans24b", "ans24c", "num24b", "num24c", "num25", "num25a", "ans25a", "ans25b", "ans25c", "ans25d", "num26a", "num26b", "ans26a", "ans26b", "ans26c"], "tags": ["rebelmaths"], "advice": "<p><img src=\"resources/question-resources/5041109_orig.png\" width=\"369\" height=\"220\"/></p>\n<p>Part 1</p>\n<p>For the first part follow the sixth rule.</p>\n<p>Example:</p>\n<p>$27^{\\frac{2}{3}} = (27^{\\frac{1}{3}})^2 = (3)^2 = 9$</p>\n<p></p>\n<p>Part 2</p>\n<p>Using most of the rules above, the following are examples of the questions in part 2 of the question.</p>\n<p>$x^3.x^5 =&nbsp;x^8$ &nbsp;<em>(Add the powers)</em></p>\n<p>$\\frac{x^{4}.x^{-2}}{x^{13}} = x^{-11}$&nbsp;<em>(Add the powers above the line and subtract the powers below the line)</em></p>\n<p>$\\frac{a^{-2}.b^{3}.c^{4}}{a^{5}.b^{-6}.c^{-4}} = a^{-7}.b^{9}.c^{8}$&nbsp;<em>(Add the powers, of the same letters, above the line and subtract the powers, of the same letters, below the line)</em></p>\n<p>$(27x^{3}y^{-6})^{\\frac{1}{3}} = 3xy^{-2}$ <em>(Use the sixth rule above)</em></p>\n<p>$3a^{-2}b^{3}c)^2 = 9a^{-4}b^{6}c^2$&nbsp;<em>(Use the sixth rule above)</em></p>\n<p>$\\frac{2^{5}.9^{2}.7^{5}}{4^{2}.8^{3}.3^{5}.49^{2}} = 2^{-8}.3^{1}.7^{1}$&nbsp;<em>(Use the first, second and third&nbsp;rules above)</em></p>", "rulesets": {}, "parts": [{"prompt": "<p>Write each of the following in its simplest form, without using a calculator:</p>\n<p></p>\n<p>i) $\\var{ans11a}^{\\frac{1}{\\var{num11[0]}}}$</p>\n<p>[[0]]</p>\n<p>ii) $\\var{ans12a}^{\\frac{\\var{num11[1]}}{\\var{num12[0]}}}$</p>\n<p>[[1]]</p>\n<p>iii) $\\var{ans13a}^{\\frac{1}{\\var{num11[1]}}}$</p>\n<p>[[2]]</p>\n<p>iv) $\\var{ans14a}^{\\frac{\\var{num11[0]}}{\\var{num12[1]}}}$</p>\n<p>[[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}", "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}", "minValue": "{ans12}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans13}", "minValue": "{ans13}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans14}", "minValue": "{ans14}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Simplify&nbsp;each of the following, without using a calculator:</p>\n<p></p>\n<p>i) $x^{\\var{num21[0]}}.x^{\\var{num21[1]}}$</p>\n<p>x^{[[0]]}</p>\n<p>ii) $\\frac{x^{\\var{num21[2]}}.x^{-\\var{num21[3]}}}{x^{\\var{num22}}}$</p>\n<p>x^{[[1]]}</p>\n<p>iii)&nbsp;$\\frac{a^{-\\var{num23[0]}}.b^{\\var{num23[1]}}.c^{\\var{num23[2]}}}{a^{\\var{num23[3]}}.b^{-\\var{num23[4]}}.c^{-\\var{num23[5]}}}$</p>\n<p>(a^{[[2]]}).(b^{[[3]]}).(c^{[[4]]})</p>\n<p>iv) $(\\var{num24a}x^{\\var{num24b}}y^{\\var{num24c}})^{\\frac{1}{3}}$</p>\n<p>[[5]](x^{[[6]]})(y^{[[7]]})</p>\n<p>v) $(\\var{num25a}a^{-\\var{num25[0]}}b^{\\var{num25[1]}}c)^\\var{num25[2]}$</p>\n<p>[[8]](a^{[[9]]})(b^{[[10]]})(c^{[[11]]})</p>\n<p>vi) $\\frac{2^{\\var{num26a[0]}}.27^{\\var{num26a[1]}}.7^{\\var{num26a[2]}}}{4^{\\var{num26b[0]}}.8^{\\var{num26b[1]}}.3^{\\var{num26b[2]}}.49^{\\var{num26b[3]}}}$</p>\n<p>(2^{[[12]]}).(3^{[[13]]}).(7^{[[14]]})</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans23a}", "minValue": "{ans23a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans23b}", "minValue": "{ans23b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans23c}", "minValue": "{ans23c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans24a}", "minValue": "{ans24a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans24b}", "minValue": "{ans24b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans24c}", "minValue": "{ans24c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans25a}", "minValue": "{ans25a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans25b}", "minValue": "{ans25b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans25c}", "minValue": "{ans25c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans25d}", "minValue": "{ans25d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans26a}", "minValue": "{ans26a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans26b}", "minValue": "{ans26b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans26c}", "minValue": "{ans26c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Writing Indices in their simplest form</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"ans13a": {"definition": "(random(2..4))^num11[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13a", "description": ""}, "ans22": {"definition": "num21[2]-num21[3]-num22", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "num21[0]+num21[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "ans26b": {"definition": "(3*num26a[1])-num26b[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans26b", "description": ""}, "ans26c": {"definition": "num26a[2]-(2*num26b[3])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans26c", "description": ""}, "num23": {"definition": "shuffle(2..7)[0..6]", "templateType": "anything", "group": "Ungrouped variables", "name": "num23", "description": ""}, "num22": {"definition": "random(10..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "num22", "description": ""}, "num21": {"definition": "shuffle(2..5)[0..4]", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "ans26a": {"definition": "num26a[0]-(2*num26b[0])-(3*num26b[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans26a", "description": ""}, "num25": {"definition": "shuffle(2..4)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "num25", "description": ""}, "num26b": {"definition": "shuffle(2..5)[0..4]", "templateType": "anything", "group": "Ungrouped variables", "name": "num26b", "description": ""}, "ans24a": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans24a", "description": ""}, "ans24b": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans24b", "description": ""}, "ans24c": {"definition": "random(1..4 except ans24b)*-1", "templateType": "anything", "group": "Ungrouped variables", "name": "ans24c", "description": ""}, "num26a": {"definition": "shuffle(2..5)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "num26a", "description": ""}, "ans12": {"definition": "ans12a^(num11[1]/num12[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans13": {"definition": "ans13a^(1/num11[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13", "description": ""}, "ans11": {"definition": "ans11a^(1/num11[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans14": {"definition": "ans14a^(num11[0]/num12[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans14", "description": ""}, "ans12a": {"definition": "(random(2..4))^num12[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12a", "description": ""}, "ans14a": {"definition": "(random(2..4))^num12[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans14a", "description": ""}, "ans11a": {"definition": "(random(2..4))^num11[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11a", "description": ""}, "ans23a": {"definition": "-num23[0]-num23[3]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23a", "description": ""}, "ans23c": {"definition": "num23[2]+num23[5]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23c", "description": ""}, "ans23b": {"definition": "num23[1]+num23[4]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23b", "description": ""}, "num24a": {"definition": "ans24a^3", "templateType": "anything", "group": "Ungrouped variables", "name": "num24a", "description": ""}, "num24b": {"definition": "ans24b*3", "templateType": "anything", "group": "Ungrouped variables", "name": "num24b", "description": ""}, "num24c": {"definition": "ans24c*3", "templateType": "anything", "group": "Ungrouped variables", "name": "num24c", "description": ""}, "num12": {"definition": "shuffle(2..4)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num25a": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num25a", "description": ""}, "num11": {"definition": "shuffle(2..4)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "ans25c": {"definition": "num25[1]*num25[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans25c", "description": ""}, "ans25b": {"definition": "-num25[0]*num25[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans25b", "description": ""}, "ans25a": {"definition": "num25a^num25[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans25a", "description": ""}, "ans25d": {"definition": "num25[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans25d", "description": ""}}, "metadata": {"description": "<p>Indices in their simples form</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q2 Indices in their simplest form 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num11", "num111", "ans11", "num12", "num121", "ans12a", "ans12b", "num131", "num132", "ans13a", "num13", "ans13b", "ans13c", "ans13d", "num141", "num142", "ans14a1", "ans14b", "num143", "num14", "ans14c", "ans14d", "ans14aT", "num21", "num211", "ans21a", "ans21b", "ans21c", "ans21d", "ans21e", "num22", "num221", "ans22a", "ans22b", "ans22c", "ans22d", "ans22e", "num31", "ans31", "num32", "ans32", "num321", "num33", "ans33a", "ans33b", "ans33c", "ans33d", "ans33e", "ans14a"], "tags": ["rebelmaths"], "advice": "<p>The following questions show the method to use to solve the above questions:</p>\n<p>Part a)</p>\n<p>i) $[\\frac{3^2.2^4}{3^{-2}.2^5}]^2$</p>\n<p>$[\\frac{3^2}{3^{-2}}]^2.[\\frac{2^4}{2^5}]^2$</p>\n<p>$[3^4]^2.[2^{-1}]^2 = 3^6.2^{-2}$</p>\n<p>ii) $[\\frac{5^3.7^2}{5^{2}.7^4}]^{-1}$</p>\n<p>$[5^1]^{-1}.[7^{-2}]^{-1} = 5^{-1}.7^2$</p>\n<p>iii) $\\frac{24x^2.y^{-4}.z^3}{8x^3.y^7.z^{-3}}$</p>\n<p>$\\frac{24}{8}.x^{2-3}.y^{-4-7}.z^{3+3} = 3.x^{-1}.y^{-11}.z^{6}$</p>\n<p>iv) $[\\frac{3a^2.b^{3}.c^{-2}}{2a^4.b.c^{2}}]^2$</p>\n<p>$[\\frac{3}{2}]^2.[a^{2-4}]^2.[b^{3-1}]^2.[c^{-2-2}]^2 = \\frac{9}{4}.a^{-4}.b^{4}.c^{-8}$</p>\n<p></p>\n<p>Part b)</p>\n<p>i)&nbsp;$\\frac{5x^3.y^{4}.z}{2x^5.y^2.z^{3}} \\times \\frac{3x^7.y^{2}.z^{-5}}{x^{-8}.y^5.z}$</p>\n<p>$\\frac{5 \\times 3}{2}.x^{3-5+7+8}.y^{4-2+2-5}.z^{1-3-5-1} = \\frac{15}{2}.x^{13}.y^{-5}.z^{-8}$</p>\n<p>ii) $\\frac{3a^5.b^{-2}.c^{7}}{2a.b^{-3}.c^{5}} \\div \\frac{a^4.b^{3}.c}{a^{-2}.b^6.c^{-1}}$</p>\n<p>$\\frac{3}{2}.a^{5-1+4+2}.b^{-2+3+3-6}.c^{7-5+1+1} = \\frac{3}{2}.a^{10}.b^{-2}.c^{4}$</p>\n<p>iii) $4^{\\frac{3}{2}}.8^{\\frac{2}{3}}.16^{\\frac{-3}{4}}$</p>\n<p>$2^{\\frac{3 \\times2}{2}}.2^{\\frac{2 \\times3}{3}}.2^{\\frac{-3 \\times4}{4}}$</p>\n<p>$2^{3+2-3} = 2^2$</p>\n<p>iv) $[\\frac{49a^4.b^{-3}.c}{25a^{-2}.b^{3}.c^{5}}]^{\\frac{1}{2}}$</p>\n<p>$[\\frac{49}{25}]^{\\frac{1}{2}}.[a^{4+2}]^{\\frac{1}{2}}.[b^{-3-3}]^{\\frac{1}{2}}.[c^{1-5}]^{\\frac{1}{2}} = \\frac{7}{5}.a^{3}.b^{-3}.c^{-2}$</p>", "rulesets": {}, "parts": [{"prompt": "<p>Simplify each of the following, without using a calculator:</p>\n<p>i)&nbsp;$[\\frac{3^{\\var{num11[0]}}.9^{\\var{num11[1]}}}{3^{-\\var{num11[2]}}.27^{\\var{num11[3]}}}]^{\\var{num111}}$</p>\n<p>${ans}^{power} =$ {[[0]]}^{[[1]]}</p>\n<p>ii)&nbsp;$[\\frac{5^{\\var{num12[0]}}.7^{\\var{num12[1]}}}{5^{\\var{num12[2]}}.7^{\\var{num12[3]}}}]^{-\\var{num121}}$</p>\n<p>${ans}^{power} =$ {[[2]]}^{[[3]]} {[[4]]}^{[[5]]}</p>\n<p>iii)&nbsp;$\\frac{\\var{num132}x^{\\var{num13[0]}}.y^{-\\var{num13[1]}}.z^{\\var{num13[2]}}}{\\var{num131}x^{\\var{num13[3]}}.y^{\\var{num13[4]}}.z^{-\\var{num13[5]}}}$</p>\n<p>${ans}^{power} =$ {[[6]]}&nbsp;x^{[[7]]} y^{[[8]]} z^{[[9]]}</p>\n<p>iv)&nbsp;$(\\frac{\\var{num142}a^{\\var{num14[0]}}.b^{-\\var{num14[1]}}.c^{-\\var{num14[2]}}}{\\var{num141}a^{\\var{num14[3]}}.b.c^{\\var{num14[4]}}})^{\\var{num143}}$</p>\n<p>${ans}^{power} =$ {[[10]]}&nbsp;a^{[[11]]} b^{[[12]]} c^{[[13]]}</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "3", "minValue": "3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}", "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "5", "minValue": "5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans12a}", "minValue": "{ans12a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "7", "minValue": "7", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans12b}", "minValue": "{ans12b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans13a}", "minValue": "{ans13a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans13b}", "minValue": "{ans13b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans13c}", "minValue": "{ans13c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans13d}", "minValue": "{ans13d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans14a}", "minValue": "{ans14a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans14b}", "minValue": "{ans14b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans14c}", "minValue": "{ans14c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans14d}", "minValue": "{ans14d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Simplify each of the following, without using a calculator:</p>\n<p>i)&nbsp;$\\frac{\\var{num211[0]}x^{\\var{num21[0]}}.y^{\\var{num21[1]}}.z}{\\var{num211[1]}x^{\\var{num21[2]}}.y^{\\var{num21[3]}}.z^{\\var{num21[4]}}} \\times \\frac{\\var{num211[2]}x^{\\var{num21[5]}}.y^{\\var{num21[6]}}.z^{-\\var{num21[7]}}}{x^{-\\var{num21[8]}}.y^{\\var{num21[9]}}.z}$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>\n<p>{<em>Fraction part</em>}${ans}^{power}$ ={&nbsp;[[0]]/[[1]]}x^{[[2]]} y^{[[3]]} z^{[[4]]}</p>\n<p></p>\n<p>ii)&nbsp;$\\frac{\\var{num221[0]}a^{\\var{num22[0]}}.b^{-\\var{num22[1]}}.c^{\\var{num22[2]}}}{\\var{num221[1]}a.b^{-\\var{num22[3]}}.c^{\\var{num22[4]}}} \\div \\frac{a^{-\\var{num22[7]}}.b^{\\var{num22[8]}}.c^{-\\var{num22[9]}}}{\\var{num221[2]}a^{\\var{num22[5]}}.b^{\\var{num22[6]}}.c}$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>\n<p>{<em>Fraction part</em>}${ans}^{power}$ = {[[5]]/[[6]]}a^{[[7]]} b^{[[8]]} c^{[[9]]}</p>\n<p>iii) $4^{\\frac{\\var{num31[0]}}{2}}.8^{\\frac{\\var{num31[1]}}{3}}.16^{\\frac{-\\var{num31[2]}}{4}}$</p>\n<p>${ans}^{power}$ = {[[10]]}^{[[11]]}</p>\n<p>iv) $27^{\\frac{\\var{num32[0]}}{3}}.8^{\\frac{-\\var{num32[1]}}{3}}.16^{\\frac{\\var{num32[2]}}{4}}$</p>\n<p>{ans}^{power} = {[[12]]}^{[[13]]}.{[[14]]}^{[[15]]}</p>\n<p>v)&nbsp;$[\\frac{\\var{num321[0]}a^{\\var{num33[0]}}.b^{-\\var{num33[1]}}.c}{\\var{num321[1]}a^{-\\var{num33[2]}}.b^{\\var{num33[3]}}.c^{\\var{num33[4]}}}]^{\\frac{1}{2}}$</p>\n<p>{<em>Fraction part</em>}${ans}^{power}$ = {[[16]]}/{[[17]]} a^{[[18]]}b^{[[19]]}c^{[[20]]}</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21a}", "minValue": "{ans21a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21b}", "minValue": "{ans21b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21c}", "minValue": "{ans21c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": true, "variableReplacements": [], "maxValue": "{ans21d}", "minValue": "{ans21d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21e}", "minValue": "{ans21e}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22a}", "minValue": "{ans22a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22b}", "minValue": "{ans22b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22c}", "minValue": "{ans22c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22d}", "minValue": "{ans22d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22e}", "minValue": "{ans22e}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "2", "minValue": "2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "3", "minValue": "3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{num32[0]}", "minValue": "{num32[0]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "2", "minValue": "2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans33a}", "minValue": "{ans33a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans33b}", "minValue": "{ans33b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans33c}", "minValue": "{ans33c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans33d}", "minValue": "{ans33d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans33e}", "minValue": "{ans33e}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Break each individual number down to a simple power first and then combine together.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "<p>Simplify the Indices</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"num221": {"definition": "shuffle(3..7 except[4,6])[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "num221", "description": ""}, "num321": {"definition": "shuffle([25,49,81,121,169])[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "num321", "description": ""}, "num143": {"definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "num143", "description": ""}, "num142": {"definition": "num131*ans14a1", "templateType": "anything", "group": "Ungrouped variables", "name": "num142", "description": ""}, "num141": {"definition": "random(2,4,8,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num141", "description": ""}, "num14": {"definition": "shuffle(2..9)[0..5]", "templateType": "anything", "group": "Ungrouped variables", "name": "num14", "description": ""}, "ans13b": {"definition": "num13[0]-num13[3]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13b", "description": ""}, "ans13c": {"definition": "-num13[1]-num13[4]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13c", "description": ""}, "ans13a": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13a", "description": ""}, "ans13d": {"definition": "num13[2]+num13[5]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13d", "description": ""}, "ans14d": {"definition": "(-num14[2]-num14[4])*num143", "templateType": "anything", "group": "Ungrouped variables", "name": "ans14d", "description": ""}, "ans12b": {"definition": "(num12[1]-num12[3])*(-num121)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12b", "description": ""}, "num121": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "num121", "description": ""}, "num32": {"definition": "shuffle(2..8)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "num32", "description": ""}, "ans22d": {"definition": "-num22[1]+num22[3]+num22[6]-num22[8]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22d", "description": ""}, "ans22e": {"definition": "num22[2]-num22[4]+1+num22[9]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22e", "description": ""}, "ans22b": {"definition": "num221[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22b", "description": ""}, "ans22c": {"definition": "num22[0]-1+num22[5]+num22[7]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22c", "description": ""}, "ans22a": {"definition": "num221[0]*num221[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22a", "description": ""}, "num22": {"definition": "shuffle(2..11)[0..10]", "templateType": "anything", "group": "Ungrouped variables", "name": "num22", "description": ""}, "num21": {"definition": "shuffle(2..11)[0..10]", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num12": {"definition": "shuffle(2..5)[0..4]", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "ans14a1": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans14a1", "description": ""}, "num13": {"definition": "shuffle(2..9)[0..6]", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num211": {"definition": "shuffle(3..7 except[4,6])[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "num211", "description": ""}, "ans11": {"definition": "(num11[0]+(2*num11[1])+num11[2]-(3*num11[3]))*num111", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans12a": {"definition": "(num12[0]-num12[2])*(-num121)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12a", "description": ""}, "ans31": {"definition": "num31[0]+num31[1]-num31[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "-num31[1]+num31[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans14aT": {"definition": "ans14a1^num143", "templateType": "anything", "group": "Ungrouped variables", "name": "ans14aT", "description": ""}, "ans14c": {"definition": "(-num14[1]-1)*num143", "templateType": "anything", "group": "Ungrouped variables", "name": "ans14c", "description": ""}, "ans14b": {"definition": "(num14[0]-num14[3])*num143", "templateType": "anything", "group": "Ungrouped variables", "name": "ans14b", "description": ""}, "ans14a": {"definition": "(num142/num141)^num143", "templateType": "anything", "group": "Ungrouped variables", "name": "ans14a", "description": ""}, "num111": {"definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "num111", "description": ""}, "num132": {"definition": "num131*ans13a", "templateType": "anything", "group": "Ungrouped variables", "name": "num132", "description": ""}, "num131": {"definition": "random(2,4,8,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num131", "description": ""}, "num31": {"definition": "shuffle(2..8)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "num31", "description": ""}, "ans21e": {"definition": "1-num21[4]-num21[7]-1", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21e", "description": ""}, "ans21d": {"definition": "num21[1]-num21[3]+num21[6]-num21[9]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21d", "description": ""}, "ans21c": {"definition": "num21[0]-num21[2]+num21[5]+num21[8]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21c", "description": ""}, "ans21b": {"definition": "num211[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21b", "description": ""}, "ans21a": {"definition": "num211[0]*num211[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21a", "description": ""}, "num11": {"definition": "shuffle(2..5)[0..4]", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "ans33d": {"definition": "(-num33[1]-num33[3])/2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33d", "description": ""}, "ans33e": {"definition": "(1-num33[4])/2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33e", "description": ""}, "num33": {"definition": "shuffle(2..8)[0..5]", "templateType": "anything", "group": "Ungrouped variables", "name": "num33", "description": ""}, "ans33a": {"definition": "sqrt(num321[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33a", "description": ""}, "ans33b": {"definition": "sqrt(num321[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33b", "description": ""}, "ans33c": {"definition": "(num33[0]+num33[2])/2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33c", "description": ""}}, "metadata": {"description": "<p>Indices in their simplest form</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q3 Indices; Solve for x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num11", "num12", "num13", "nn1", "p1", "ans1", "num21", "num22", "p21", "p22", "nn21", "nn22", "ans2", "p31", "p32", "num31", "num32", "ans3", "p41", "p42", "num41", "num42", "num43", "ans4", "nn31", "nn32", "nn41", "nn42"], "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>i) $2^{4x-3} = 4^{x+1}$</p>\n<p>$2^{4x-3} = 2^{2x+2}$</p>\n<p>$4x-3 = 2x+2$</p>\n<p>$4x-2x = 3+2$</p>\n<p>$x = \\frac{5}{2}$</p>\n<p></p>\n<p>ii) $9^{x-4} = 27^{2-x}$</p>\n<p>$3^{2x-8} = 3^{6-3x}$</p>\n<p>$2x-8 = 6-3x$</p>\n<p>$2x+3x = 6+8$</p>\n<p>$x = \\frac{14}{5}$</p>\n<p></p>\n<p>iii) $2^{2x+3} = \\frac{1}{4}$</p>\n<p>$2^{2x+3} = 2^{-2}$</p>\n<p>$2x+3 = -2$</p>\n<p>$2x = -2-3$</p>\n<p>$x = \\frac{-5}{2}$</p>\n<p></p>\n<p>iv) $25^{2x-3} = 5^{4-x}$</p>\n<p>$5^{4x-6} = 5^{4-x}$</p>\n<p>$4x-6 =&nbsp;4-x$</p>\n<p>$4x+x = 4+6$</p>\n<p>$x = 2$</p>", "rulesets": {}, "parts": [{"prompt": "<p>$2^{\\var{num11}x-\\var{num12}} = \\var{nn1}^{x+\\var{num13}}$</p>\n<p>x =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{nn21}^{x-\\var{num21}} = \\var{nn22}^{\\var{num22} - x}$</p>\n<p>x=&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{nn31}^{\\var{num31}x+\\var{num32}} = \\frac{1}{\\var{nn32}}$</p>\n<p>x&nbsp;=&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{nn41}^{\\var{num41}x-\\var{num42}} = \\var{nn42}^{\\var{num43} - x}$</p>\n<p>x&nbsp;=&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve for x in each of the following:</p>\n<p><em>Enter answer as whole number or fraction</em></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "(num12+num13*p1)/(num11-p1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(num22*p22+num21*p21)/(p21+p22)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "((p32*-1)-num32*p31)/(p31*num31)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "((p42*num43)+num42*p41)/((p41*num41)+p42)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "p21": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p21", "description": ""}, "p22": {"definition": "random(1..3 except p21)", "templateType": "anything", "group": "Ungrouped variables", "name": "p22", "description": ""}, "p42": {"definition": "random(1..3 except p41)", "templateType": "anything", "group": "Ungrouped variables", "name": "p42", "description": ""}, "p41": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p41", "description": ""}, "nn22": {"definition": "3^(p22)", "templateType": "anything", "group": "Ungrouped variables", "name": "nn22", "description": ""}, "nn21": {"definition": "3^(p21)", "templateType": "anything", "group": "Ungrouped variables", "name": "nn21", "description": ""}, "num22": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num22", "description": ""}, "num21": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num41": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num41", "description": ""}, "num43": {"definition": "random(3..6 except [num41,num42])", "templateType": "anything", "group": "Ungrouped variables", "name": "num43", "description": ""}, "num42": {"definition": "random(3..6 except num41)", "templateType": "anything", "group": "Ungrouped variables", "name": "num42", "description": ""}, "nn41": {"definition": "5^p41", "templateType": "anything", "group": "Ungrouped variables", "name": "nn41", "description": ""}, "nn42": {"definition": "5^p42", "templateType": "anything", "group": "Ungrouped variables", "name": "nn42", "description": ""}, "p32": {"definition": "random(1..3 except p31)", "templateType": "anything", "group": "Ungrouped variables", "name": "p32", "description": ""}, "p31": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p31", "description": ""}, "nn1": {"definition": "2^(p1)", "templateType": "anything", "group": "Ungrouped variables", "name": "nn1", "description": ""}, "p1": {"definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "nn31": {"definition": "2^p31", "templateType": "anything", "group": "Ungrouped variables", "name": "nn31", "description": ""}, "nn32": {"definition": "2^p32", "templateType": "anything", "group": "Ungrouped variables", "name": "nn32", "description": ""}, "num12": {"definition": "random(3..5 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num13": {"definition": "random(1..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num11": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "num31": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num31", "description": ""}, "num32": {"definition": "random(3..6 except num31)", "templateType": "anything", "group": "Ungrouped variables", "name": "num32", "description": ""}}, "metadata": {"description": "<p>Indices</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Deirdre Casey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/681/"}], "extensions": [], "custom_part_types": [], "resources": [["question-resources/5041109_orig.png", "/srv/numbas/media/question-resources/5041109_orig.png"]]}