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{"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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"], "name": "Q1 Indices in their simplest form 1", "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"}], "extensions": [], "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": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}