// Numbas version: exam_results_page_options
{"name": "1.2.5.2 Simplify expression with fractional indices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.2.5.2 Simplify expression with fractional indices", "tags": [], "metadata": {"description": "<p>Simplify (a^k1*a^k2)/(a^k3*a^k4) where a is a randomised variable and k1,k2,k3 and k4 are randomised fractions (k2 and/or k4 may be 0). They may be written in index form or in surd form, or even a combination of the two.</p>\n<p>Part of HELM Book 1.2</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify $\\displaystyle{ \\var{expr} }$</p>", "advice": "<p>The basic approach is to:</p>\n<p>(a) convert surds to indices</p>\n<p>(b) add the indices on the numerator, and subtract indices on the denominator.</p>\n<p>\\[&nbsp; \\var{expr} = \\frac{\\var{adviceNum[0]}}{\\var{adviceDen}}= \\var{adviceNum[1]}=\\var{ans} \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"expr": {"name": "expr", "group": "Ungrouped variables", "definition": "latex(\"\\\\frac\\{\"+num+\"\\}\\{\"+den+\"\\}\")", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "expression(q3letter+\"^(\"+ 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variables", "definition": "switch(T2idx=0,\"\",\n  T2idx=1,q3letter,\n  T2idx=1/2,\"\\\\sqrt\\{\" + q3letter + \"\\}\",\n  T2idx=1/3,\"\\\\sqrt\\[3]{\" + q3letter + \"\\}\",\n  T2idx=1/4,\"\\\\sqrt\\[4]{\" + q3letter + \"\\}\",\n  q3letter + \"^\\{\" + q3T2idxStr + \"\\}\"\n  )", "description": "", "templateType": "anything", "can_override": false}, "q3t4idxstr": {"name": "q3t4idxstr", "group": "Ungrouped variables", "definition": "string(simplify(expression(string(T4idx)),[\"simplifyFractions\",\"basic\",\"unitFactor\",\"unitDenominator\"]))", "description": "", "templateType": "anything", "can_override": false}, "idxfracs": {"name": "idxfracs", "group": "Ungrouped variables", "definition": "eval(expression(random(-1,1)+\"*\"+(random(1..5)/random(1..9))))", "description": "", "templateType": "anything", "can_override": false}, "idxsurds": {"name": "idxsurds", "group": "Ungrouped variables", "definition": "[1/2,1/3,1/4]", "description": "", "templateType": "anything", "can_override": false}, "q3t3idxstr": {"name": "q3t3idxstr", "group": "Ungrouped variables", "definition": "string(simplify(expression(string(T3idx)),[\"simplifyFractions\",\"basic\",\"unitFactor\",\"unitDenominator\"]))", "description": "", "templateType": "anything", "can_override": false}, "q3t2idxstr": {"name": "q3t2idxstr", "group": "Ungrouped variables", "definition": "string(simplify(expression(string(T2idx)),[\"simplifyFractions\",\"basic\",\"unitFactor\",\"unitDenominator\"]))", "description": "", "templateType": "anything", "can_override": false}, "q3t1idxstr": {"name": "q3t1idxstr", "group": "Ungrouped variables", "definition": "string(simplify(expression(string(T1idx)),[\"simplifyFractions\",\"basic\",\"unitFactor\",\"unitDenominator\"]))", "description": "", "templateType": "anything", "can_override": false}, "adviceNum": {"name": "adviceNum", "group": "Ungrouped variables", "definition": "[if(T1idx=0,\n  expression(q3letter+\"^(\"+T2idx+\")\"),\n  expression(q3letter+\"^(\"+t1idx + 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