// Numbas version: exam_results_page_options
{"name": "Indices: Change of Notation 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Indices: Change of Notation 1", "tags": ["category: Indices", "leads to: Bb", "skill: Ba"], "metadata": {"description": "<p>Rewriting expressions from $\\sqrt[m]{x^n}$ to $x^\\frac{n}{m}$.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Rewrite the following expression in the form $x^n$, where $n$ is an integer or a fraction</p>\n<p>\\[ \\simplify{root(x^{n},{m})}\\]</p>", "advice": "<p>To rewrite $\\sqrt[\\var{m}]{x^\\var{n}}$ in the form $x^n$, we need to use the following 2 rules:</p>\n<ol>\n<li>$\\sqrt[n]{a} = a^{1/n}$;</li>\n<li>$\\left(a^n\\right)^m = a^{n \\times m}$.</li>\n</ol>\n<p>Applying rule 1:</p>\n<p>\\[\\sqrt[\\var{m}]{x^\\var{n}} = \\left(x^\\var{n}\\right)^\\simplify[fractionNumbers]{{1/m}}.\\]</p>\n<p>Then applying rule 2 and simplifying:</p>\n<p>\\[ \\begin{split}\\left(x^\\var{n}\\right)^\\simplify[fractionNumbers]{{1/m}} &amp;\\,= x^{\\var{n} \\times \\simplify[fractionNumbers]{{1/m}}} \\\\ &amp;\\,=x^{\\simplify[fractionNumbers]{{n/m}}}. \\end{split} \\]</p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..5 except n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "m"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "x^({n/m})", "answerSimplification": "fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "x^`+-rational:$n", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ed Southwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2415/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ed Southwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2415/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}