// Numbas version: exam_results_page_options
{"name": "Algebra IV: Properties of indices (3) - Negative integers/fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "f1", "f2", "f3", "f4", "t1", "t2", "sar", "sar2", "sar3", "sar4"], "name": "Algebra IV: Properties of indices (3) - Negative integers/fractions", "tags": [], "advice": "<p>Recall the laws of indices to help solve the problems:</p>\n<ul>\n<li style=\"text-align: left;\">$x^a \\times x^b = x^{a+b}$</li>\n<li style=\"text-align: left;\">$x^a \\div x^b = x^{a-b}$</li>\n<li style=\"text-align: left;\">$x^{-a} = \\frac{1}{x^a}$</li>\n<li style=\"text-align: left;\">$(x^a)^b = x^{ab}$</li>\n<li style=\"text-align: left;\">$(\\frac{x}{y})^a = \\frac{x^a}{y^a}$</li>\n<li style=\"text-align: left;\">$x^0 = 1$</li>\n<li style=\"text-align: left;\">$x^\\frac{a}{b} = (\\sqrt[b]{x})^{a}$</li>\n<li><strong>$x^{\\simplify{-a/b}}$ = $\\frac{1}{(\\sqrt[b]{x})^{a}}$</strong></li>\n<li><strong>$x^{-a} = \\frac{1}{x^{a}}$</strong></li>\n</ul>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$\\var{c}^{\\simplify{-1/{b}}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "1/2", "minValue": "1/2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>This question can alternatively be considered as being :</p>\n<p>$a^{\\simplify{-1/b}}$ = $\\frac{1}{\\sqrt[b]{a}}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>$\\var{d}^{\\simplify{-1/{a}}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "1/3", "minValue": "1/3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>This question can alternatively be considered as being :</p>\n<p>$a^{\\simplify{-1/b}}$ = $\\frac{1}{\\sqrt[b]{a}}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>$\\var{h}^{\\simplify{-{f}/{g}}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "3^-{f}", "minValue": "3^-{f}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>This question can alternatively be considered as being :</p>\n<p>$a^{\\simplify{-c/b}}$ = $\\frac{1}{(\\sqrt[b]{a})^{c}}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>$\\var{l}^{\\simplify{-{k}/{j}}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "2^-k", "minValue": "2^-k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>This question can alternatively be considered as being :</p>\n<p>$a^{\\simplify{-c/b}}$ = $\\frac{1}{(\\sqrt[b]{a})^{c}}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>$\\var{f3}^{\\simplify{-{f1}/{f2}}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "5^-f1", "minValue": "5^-f1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "steps": [{"prompt": "<p>This question can alternatively be considered as being :</p>\n<p>$a^{\\simplify{-c/b}}$ = $\\frac{1}{(\\sqrt[b]{a})^{c}}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "precisionType": "dp", "prompt": "<p>$(\\var{sar}/\\var{sar2})^{-2}$</p>\n<p>Give your answer to the nearest whole number</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": true, "variableReplacements": [], "precision": 0, "maxValue": "({sar}/{sar2})^-2", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "steps": [{"prompt": "<p>Firstly, you need to consider BODMAS and how this affects the above expression.</p>\n<p>Using laws of indices:</p>\n<p>$x^{-a}$ = $\\frac{1}{x^{a}}$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "precisionPartialCredit": 0, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "minValue": "({sar}/{sar2})^-2", "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "precisionType": "dp", "prompt": "<p>$(\\var{sar3}/\\var{sar4})^{-4}$</p>\n<p>Give your answer to the nearest whole number</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": true, "variableReplacements": [], "precision": 0, "maxValue": "({sar3}/{sar4})^-4", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "steps": [{"prompt": "<p>Firstly, you need to consider BODMAS and how this affects the above expression.</p>\n<p>Using laws of indices:</p>\n<p>$x^{-a}$ = $\\frac{1}{x^{a}}$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "precisionPartialCredit": 0, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "minValue": "({sar3}/{sar4})^-4", "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>Simplify the following questions, giving your answer in its simplest form (as a fraction - unless asked otherwise).</p>\n<p>Recall:</p>\n<ul>\n<li><strong>$x^{\\simplify{-a/b}}$ = $\\frac{1}{(\\sqrt[b]{x})^{a}}$</strong></li>\n<li><strong>$x^{-a} = \\frac{1}{x^{a}}$</strong></li>\n</ul>\n<p>You may need a calculator for some of the questions.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "gcd({k},{j})=1"}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "f1": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "c": {"definition": "2^b", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "f4": {"definition": "5^f1", "templateType": "anything", "group": "Ungrouped variables", "name": "f4", "description": ""}, "d": {"definition": "3^a", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(2..4 except f)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "3^g", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(2..5 except j)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "t2": {"definition": "3^f2", "templateType": "anything", "group": "Ungrouped variables", "name": "t2", "description": ""}, "l": {"definition": "2^j", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "f2": {"definition": "random(2..4 except f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "t1": {"definition": "2^f2", "templateType": "anything", "group": "Ungrouped variables", "name": "t1", "description": ""}, "f3": {"definition": "5^f2", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "sar": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "sar", "description": ""}, "sar2": {"definition": "random(12..25)", "templateType": "anything", "group": "Ungrouped variables", "name": "sar2", "description": ""}, "sar3": {"definition": "random(2..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "sar3", "description": ""}, "sar4": {"definition": "random(15..30)", "templateType": "anything", "group": "Ungrouped variables", "name": "sar4", "description": ""}}, "metadata": {"description": "<p>Simplifying indices</p>\n<p></p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}]}]}], "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}]}