// Numbas version: exam_results_page_options
{"name": "Index Laws 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "name": "a"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "name": "c"}, "s2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5 except t2)", "description": "", "name": "s2"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "name": "a1"}, "c2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "", "name": "c2"}, "d2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "", "name": "d2"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "t*f", "description": "", "name": "n"}, "f2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5 except [b,0])", "description": "", "name": "f2"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "name": "b"}, "n2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "t2*s2", "description": "", "name": "n2"}, "a2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "name": "a2"}, "h2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3 except [d2,0])", "description": "", "name": "h2"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "d"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a*f+b*c*f*t-d*t", "description": "", "name": "m"}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "f"}, "t2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "t2"}, "b2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-4..5 except 0)", "description": "", "name": "b2"}, "p2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "b2+c2*d2", "description": "", "name": "p2"}, "t1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..5)", "description": "", "name": "t1"}, "m2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "t2*b2+t2*c2*d2-s2*f2-s2*g2*h2", "description": "", "name": "m2"}, "q2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "f2+g2*h2", "description": "", "name": "q2"}, "g2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3 except [c2,0])", "description": "", "name": "g2"}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..5)", "description": "", "name": "t"}}, "ungrouped_variables": ["f2", "h2", "t2", "b2", "n", "d2", "q2", "s2", "m2", "a", "g2", "a1", "a2", "c2", "p2", "c", "b", "d", "f", "m", "t1", "t", "n2"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Index Laws 2", "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}], "type": "gapfill", "prompt": "\n        <p>${\\LARGE\\sqrt[\\var{t1}]{a^\\var{a1}}}$</p> <p>The power is [[0]]</p>\n      \n      ", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "{m}/{n}", "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>${\\LARGE\\dfrac{\\sqrt[\\var{t}]{a^\\var{a}}*(a^\\var{b})^{\\var{c}}}{(a^\\var{d})^{1/\\var{f}}}}$</p> <p>In lowest terms, the power is [[0]]</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}], "type": "gapfill", "prompt": "\n        <p>${\\LARGE\\dfrac{\\sqrt[\\var{s2}]{a^{\\var{b2}}*(a^{\\var{c2}})^{\\var{d2}}}}{\\sqrt[\\var{t2}]{a^{\\var{f2}}*(a^{\\var{g2}})^{\\var{h2}}}}}$</p> <p>In lowest terms, the power is [[0]]</p>\n      \n      ", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>Express the following as a power of a, writing the power in the box provided. Write the power as a fraction or as an integer.</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 a, write the n'th root as: to the power 1/n. Then apply the index laws to combine the powers. Thus \\[{\\LARGE\\sqrt[\\var{t1}]{a^\\var{a1}}=(a^\\var{a1})^{1/\\var{t1}}=a^{\\simplify{{a1}/{t1}}}},\\]\n  \\[{\\LARGE\\dfrac{\\sqrt[\\var{t}]{a^\\var{a}}*(a^\\var{b})^{\\var{c}}}{(a^\\var{d})^{1/\\var{f}}}=\\dfrac{(a^{\\var{a}})^{1/ \\var{t}} * (a^{\\var{b}})^{\\var{c}}}{(a^{\\var{d}})^{1/\\var{f}}}=\\dfrac{a^{\\var{a}/\\var{t}} * a^{\\var{b* c}}}{a^{\\var{d}/\\var{f}}}}\\] \n  \\[{\\LARGE=a^{\\var{a}/\\var{t}} * a^{\\var{b* c}}*a^{-\\var{d}/\\var{f}}=a^{\\simplify{{m}/{n}}}},\\]\n  \\[{\\LARGE\\dfrac{\\sqrt[\\var{s2}]{a^{\\var{b2}}*(a^{\\var{c2}})^{\\var{d2}}}}{\\sqrt[\\var{t2}]{a^{\\var{f2}}*(a^{\\var{g2}})^{\\var{h2}}}}=\\dfrac{(a^{\\var{b2}}*a^{\\var{c2*d2}})^{1/\\var{s2}}}{(a^{\\var{f2}}*a^{\\var{g2*h2}})^{1/\\var{t2}}}}\\]\n  \\[{\\LARGE=\\dfrac{(a^{\\var{b2+c2*d2}})^{1/\\var{s2}}}{(a^{\\var{f2+g2*h2}})^{1/\\var{t2}}}=\\dfrac{a^{\\simplify{{p2}/{s2}}}}{a^{\\simplify{{q2}/{t2}}}}=a^{\\simplify{{m2}/{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/"}]}