// Numbas version: exam_results_page_options
{"name": "Index Laws 3", "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(0..4 except b)", "description": "", "name": "c"}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..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"}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "t"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "name": "a1"}, "m3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "c*d*h*t+g*t-k*l*h*t-n*h", "description": "", "name": "m3"}, "k": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..4 except [c,g,j])", "description": "", "name": "k"}, "l": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5 except d)", "description": "", "name": "l"}, "m2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "b*d*h*t+f*t-j*l*h*t-m*h", "description": "", "name": "m2"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..4 except [c,g,k,m])", "description": "", "name": "n"}, "h": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5 except t)", "description": "", "name": "h"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..4)", "description": "", "name": "b"}, "g": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..4 except [c,f])", "description": "", "name": "g"}, "n2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "t*h", "description": "", "name": "n2"}, "j": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..4 except [b,f])", "description": "", "name": "j"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..4 except [b,f,j])", "description": "", "name": "m"}}, "ungrouped_variables": ["c", "b", "d", "g", "f", "h", "k", "j", "m", "l", "t1", "a1", "t", "m3", "m2", "n2", "n", "b1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Index Laws 3", "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>${\\LARGE\\sqrt[\\var{t1}]{\\var{2^{a1}*3^{b1}}}}$</p> <p>$\\alpha =$ [[0]], $\\beta =$ [[1]]</p>\n        \n        ", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "{m2}/{n2}", "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}/{n2}", "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>${\\LARGE\\dfrac{(\\var{2^b * 3^c})^{\\var{d}}*(\\var{2^f * 3^g})^{1/\\var{h}}}{(\\var{2^j *3^k})^{\\var{l}}*\\sqrt[\\var{t}]{\\var{2^m *3^n}}}}$</p> <p>$\\alpha =$ [[0]], $\\beta =$ [[1]]</p>\n        \n        ", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>Express the following in the form $2^{\\alpha} 3^{\\beta}$, 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 each of the numbers as a power of 2 multiplied by a power of 3, 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}]{\\var{2^{a1}*3^{b1}}}=(2^{\\var{a1}}*3^{\\var{b1}})^{1/\\var{t1}}=(2^{\\var{a1}})^{1/\\var{t1}}*(3^{\\var{b1}})^{1/\\var{t1}}=2^{\\simplify{{a1}/{t1}}} 3^{\\simplify{{b1}/{t1}}}},\\]\n    \\[{\\LARGE\\dfrac{(\\var{2^b * 3^c})^{\\var{d}}*(\\var{2^f * 3^g})^{1/\\var{h}}}{(\\var{2^j *3^k})^{\\var{l}}*\\sqrt[\\var{t}]{\\var{2^m *3^n}}}=\\dfrac{(2^{\\var{b}} * 3^{\\var{c}})^{\\var{d}}*(2^{\\var{f}} * 3^{\\var{g}})^{1/\\var{h}}}{(2^{\\var{j}} *3^{\\var{k}})^{\\var{l}}*(2^{\\var{m}} *3^{\\var{n}})^{1/\\var{t}}}}\\]\n    \\[{\\LARGE =\\dfrac{(2^{\\var{b*d}} * 3^{\\var{c*d}})*(2^{\\var{f}/\\var{h}} * 3^{\\var{g}/\\var{h}})}{(2^{\\var{j*l}} *3^{\\var{k*l}})*(2^{\\var{m}/\\var{t}} *3^{\\var{n}/\\var{t}})} =\\dfrac{2^{\\var{b*d}} * 3^{\\var{c*d}}*2^{\\var{f}/\\var{h}} * 3^{\\var{g}/\\var{h}}}{2^{\\var{j*l}} *3^{\\var{k*l}}*2^{\\var{m}/\\var{t}} *3^{\\var{n}/\\var{t}}}}\\]\n    \\[{\\LARGE =2^{\\var{b*d}} *2^{\\var{f}/\\var{h}}*2^{\\var{-j*l}}*2^{-\\var{m}/\\var{t}} * 3^{\\var{c*d}} * 3^{\\var{g}/\\var{h}} *3^{-\\var{k*l}}*3^{-\\var{n}/\\var{t}} =2^{\\simplify{{m2}/{n2}}} 3^{\\simplify{{m3}/{n2}}}}\\]\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/"}]}