// Numbas version: exam_results_page_options
{"name": " Indices - negative and fractional", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["n12", "n10", "n11", "x8", "x9", "n1", "x2", "x1", "x6", "x7", "x4", "x5", "x73", "n", "n8", "n9", "x10", "x11", "n2", "n3", "n4", "n5", "n6", "n7"], "name": " Indices - negative and fractional", "tags": ["fractional indices", "indices", "negative indices", "powers", "roots"], "advice": "<p>Recall that a fractional power indicates a root. So $x^\\frac{1}{\\var{n}}= \\sqrt[\\var{n}] x$.</p>\n<p></p>\n<p>A negative power indicates a reciprocal. For instance $ 3^{-2} = \\dfrac{1}{3^2}$.</p>", "rulesets": {"std": ["all", "fractionNumbers", "basic"]}, "parts": [{"prompt": "<p>If $ x^\\frac{1}{\\var{n}} = \\var{x1} $, find the value of $x$.</p>\n<p>$x=$ [[0]]</p>\n<p></p>\n<p></p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{x1}^{n}", "minValue": "{x1}^{n}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>If $ y^{\\simplify{{1}/{n2}}}= \\var{x2} $, find the value of $y$.</p>\n<p>Give your answer as a decimal without rounding.</p>\n<p>$y$ = [[0]]</p>\n<p>&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{x2}^{n2}", "minValue": "{x2}^{n2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Find the value of $x$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"n12": {"definition": "random(-3..-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "n12", "description": ""}, "n10": {"definition": "random(1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "n10", "description": ""}, "n11": {"definition": "random(0,2,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "n11", "description": ""}, "x8": {"definition": "random(1,3,5,7,11)", "templateType": "anything", 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"templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}, "n3": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "n3", "description": ""}, "n4": {"definition": "random(2..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "n4", "description": ""}, "n5": {"definition": "random(2..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "n5", "description": ""}, "n6": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "n6", "description": ""}, "n7": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "n7", "description": ""}}, "metadata": {"description": "<p>Given value of x^(1/n), x^(-1/n) find x.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}