// Numbas version: exam_results_page_options
{"name": "Index Laws 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "d"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4 except b)", "description": "", "name": "c"}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4 except b)", "description": "", "name": "f"}, "t1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..5)", "description": "", "name": "t1"}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "name": "b1"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "name": "a1"}, "m3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "c*d*h+g-k*l*h", "description": "", "name": "m3"}, "k": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4 except [c,g,j])", "description": "", "name": "k"}, "l": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..4 except d)", "description": "", "name": "l"}, "m2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "b*d*h+f-j*l*h", "description": "", "name": "m2"}, "h": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..3)", "description": "", "name": "h"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "name": "b"}, "g": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4 except [c,f])", "description": "", "name": "g"}, "j": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4 except [b,f])", "description": "", "name": "j"}}, "ungrouped_variables": ["c", "b", "d", "g", "f", "h", "k", "j", "l", "t1", "a1", "b1", "m3", "m2"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Index Laws 4", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"answer": "{a1}/{t1}", "vsetrange": [0, 1], "checkingaccuracy": 0.0001, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "std", "marks": 2, "vsetrangepoints": 5}, {"answer": "{b1}/{t1}", "vsetrange": [0, 1], "checkingaccuracy": 0.0001, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "std", "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "\n      <p>${\\LARGE\\sqrt[\\var{t1}]{x^{\\var{a1}}*y^{\\var{b1}}}}$</p> <p>$\\alpha =$ [[0]], $\\beta =$ [[1]]</p>\n        \n        ", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "{m2}/{h}", "vsetrange": [0, 1], "checkingaccuracy": 0.0001, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "std", "marks": 2, "vsetrangepoints": 5}, {"answer": "{m3}/{h}", "vsetrange": [0, 1], "checkingaccuracy": 0.0001, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "std", "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "\n      <p>${\\LARGE \\dfrac{(x^{\\var{b}} * y^{\\var{c}})^{\\var{d}}*(x^{\\var{f}} * y^{\\var{g}})^{1/\\var{h}}}{(x^{\\var{j}} *y^{\\var{k}})^{\\var{l}}}}$</p> <p>$\\alpha =$ [[0]], $\\beta =$ [[1]]</p>\n        \n        ", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>Express the following in the form $x^{\\alpha} y^{\\beta}$, writing the $\\alpha$ and $\\beta$ in the boxes provided. Write the powers as fractions or as integers.</p>", "tags": ["Index Laws", "SFY0001", "checked2015", "exponents", "indices", "powers"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Questions testing understanding of the index laws.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "\n    <p>Write the n'th root as: to the power 1/n. Then apply the index laws to combine the powers.\n    \n    Write each of the numbers as a power of $x$ multiplied by a power of $y$, write the n'th root as: to the power 1/n. Then apply the index laws to combine the powers. Thus\n    \\[{\\LARGE\\sqrt[\\var{t1}]{x^{\\var{a1}}*y^{\\var{b1}}}=(x^{\\var{a1}}*y^{\\var{b1}})^{1/\\var{t1}}=(x^{\\var{a1}})^{1/\\var{t1}}*(y^{\\var{b1}})^{1/\\var{t1}}=x^{\\simplify{{a1}/{t1}}} y^{\\simplify{{b1}/{t1}}}},\\]\n    \\[{\\LARGE\\dfrac{(x^{\\var{b}} * y^{\\var{c}})^{\\var{d}}*(x^{\\var{f}} * y^{\\var{g}})^{1/\\var{h}}}{(x^{\\var{j}} *y^{\\var{k}})^{\\var{l}}} =\\dfrac{(x^{\\var{b*d}} * y^{\\var{c*d}})*(x^{\\var{f}/\\var{h}} * y^{\\var{g}/\\var{h}})}{(x^{\\var{j*l}} *y^{\\var{k*l}})} }\\]\n    \\[{\\LARGE =x^{\\var{b*d}} *x^{\\var{f}/\\var{h}}*x^{\\var{-j*l}} * y^{\\var{c*d}} * y^{\\var{g}/\\var{h}} *y^{-\\var{k*l}} =x^{\\simplify{{m2}/{h}}} y^{\\simplify{{m3}/{h}}}}\\]\n    </p>\n    ", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}