// Numbas version: exam_results_page_options
{"name": "Indices: multiplying powers (non-algebraic)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Indices: multiplying powers (non-algebraic)", "advice": "", "preamble": {"js": "", "css": ""}, "statement": "<p>Simplify the following without the use of a calculator. Write your answer in index form using ^ to signify powers.</p>", "functions": {}, "rulesets": {}, "variable_groups": [], "parts": [{"prompt": "<p>$\\left(\\var{base1}^\\var{powers1}\\right)^2$ =&nbsp;[[0]]</p>", "stepsPenalty": "1", "marks": 0, "gaps": [{"answer": "{base1}^{prodpow1}", "marks": 1, "maxlength": {"partialCredit": 0, "length": "4", "message": "<p>Your answer is&nbsp;longer than necessary.</p>"}, "showpreview": true, "scripts": {"mark": {"order": "after", "script": "//commented out because a student reported a problem, not sure how to fix!\n// Parse the student's answer as a syntax tree\n//var studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\n//var rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \n//var m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\n//if(!m) {\n//  this.multCredit(0,'Your answer is not in the form $x^y$.');\n//}\n"}}, "checkingaccuracy": "0.001", "variableReplacements": [], "expectedvariablenames": [], "musthave": {"strings": ["^"], "partialCredit": 0, "showStrings": false, "message": "<p>Use ^ for powers. Input your answer in index form.</p>"}, "answersimplification": "basic", "vsetrange": [0, 1], "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "type": "jme", "vsetrangepoints": 5, "notallowed": {"strings": ["^0"], "partialCredit": 0, "showStrings": false, "message": "<p>Use ^ for powers. Input your answer in index form.</p>"}, "showCorrectAnswer": true, "checkvariablenames": false}], "steps": [{"prompt": "<p><em>Interpret the powers in expanded form and then write the result in index form.<br/></em></p>\n<hr/>\n<p>Suppose you had to simplify $(5^3)^2$. Well cubed means there are three 5s all being multiplied, so we have</p>\n<p>\\[(5^3)^2=(5\\times 5\\times 5)^2\\]</p>\n<p>and squared means multiplied by itself (in this case the square is acting on the whole bracketed term) so we get</p>\n<p>\\[(5^3)^2=(5\\times 5\\times 5)^2=(5\\times 5\\times 5)\\times (5\\times 5\\times 5)\\]</p>\n<p>&nbsp;but this is just six 5s all being multiplied together, that is</p>\n<p>\\[(5^3)^2=5^6.\\]</p>\n<hr/>\n<p>In general, we have $\\displaystyle(a^b)^c=a^{bc}$.</p>", "marks": 0, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "information"}], "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p>$\\displaystyle(\\var{base2}^\\var{powers2[0][0]})^\\var{powers2[1][0]}$ =&nbsp;[[0]]</p>\n<p></p>\n<p></p>", "stepsPenalty": "1", "marks": 0, "gaps": [{"answer": "{base2}^{prodpow2}", "marks": 1, "maxlength": {"partialCredit": 0, "length": "4", "message": "<p>Your answer is&nbsp;longer than necessary.</p>"}, "showpreview": true, "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "checkingaccuracy": "0.001", "variableReplacements": [], "expectedvariablenames": [], "musthave": {"strings": ["^"], "partialCredit": 0, "showStrings": false, "message": "<p>Use ^ for powers. Input your answer in index form.</p>"}, "answersimplification": "basic", "vsetrange": [0, 1], "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "type": "jme", "vsetrangepoints": 5, "notallowed": {"strings": ["^0"], "partialCredit": 0, "showStrings": false, "message": "<p>Use ^ for powers. Input your answer in index form.</p>"}, "showCorrectAnswer": true, "checkvariablenames": false}], "steps": [{"prompt": "<p><em>Interpret the powers in expanded form and then write the result in index form.<br/></em></p>\n<hr/>\n<p>Suppose you had to simplify $(5^3)^2$. Well cubed means there are three 5s all being multiplied, so we have</p>\n<p>\\[(5^3)^2=(5\\times 5\\times 5)^2\\]</p>\n<p>and squared means multiplied by itself (in this case the square is&nbsp;acting on the whole bracketed term) so we get</p>\n<p>\\[(5^3)^2=(5\\times 5\\times 5)^2=(5\\times 5\\times 5)\\times (5\\times 5\\times 5)\\]</p>\n<p>&nbsp;but this is just six 5s all being multiplied together, that is</p>\n<p>\\[(5^3)^2=5^6.\\]</p>\n<hr/>\n<p>In general, we have $\\displaystyle(a^b)^c=a^{bc}$.</p>", "marks": 0, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "information"}], "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p>Use the same approach you used in the above questions to simplify the following in index form.</p>\n<p><br/>$\\displaystyle\\left(\\left(\\var{base3}^\\var{powers3[0][0]}\\right)^\\var{powers3[1][0]}\\right)^\\var{powers3[2][0]}$ =&nbsp;[[0]]</p>\n<p></p>", "stepsPenalty": "1", "marks": 0, "gaps": [{"answer": "{base3}^{prodpow3}", "marks": 1, "maxlength": {"partialCredit": 0, "length": "6", "message": "<p>Your answer is&nbsp;longer than necessary.</p>"}, "showpreview": true, "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "checkingaccuracy": "0.001", "variableReplacements": [], "expectedvariablenames": [], "musthave": {"strings": ["^"], "partialCredit": 0, "showStrings": false, "message": "<p>Use ^ for powers. Input your answer in index form.</p>"}, "answersimplification": "basic", "vsetrange": [0, 1], "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "type": "jme", "vsetrangepoints": 5, "notallowed": {"strings": ["^0"], "partialCredit": 0, "showStrings": false, "message": "<p>Use ^ for powers. Input your answer in index form.</p>"}, "showCorrectAnswer": true, "checkvariablenames": false}], "steps": [{"prompt": "<p><em>Interpret the powers in expanded form and then write the result in index form.<br/></em></p>\n<hr/>\n<p>Suppose you had to simplify $((5^3)^2)^4$.&nbsp;We could start by applying the square</p>\n<p>&nbsp;\\[((5^3)^2)^4=(5^3\\times 5^3)^4=(5^6)^4\\]&nbsp;</p>\n<p>and then apply the fourth power</p>\n<p>\\[(5^6)^4=5^6\\times 5^6\\times 5^6\\times 5^6 = 5^{24}.\\]</p>\n<hr/>\n<p>Notice the above is the long way of just applying the rule&nbsp; $\\displaystyle(a^b)^c=a^{bc}$ twice:</p>\n<p>\\[((5^3)^2)^4=(5^6)^4=5^{24}.\\]</p>\n<p>In fact, we could just multiply all the powers together in one go:</p>\n<p>\\[((5^3)^2)^4=5^{3\\times 2\\times 4}=5^{24}.\\]</p>", "marks": 0, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "information"}], "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p><br/>$\\displaystyle\\left(\\left(\\var{base4}^\\var{nint}\\right)^\\var{ndec}\\right)^{\\var{num}/\\var{den}}$ =&nbsp;[[0]]</p>\n<p></p>\n<p>Note: If you want to use a fraction as a power you should use brackets to surround your power, for example, type 12^(2/3) for $12^\\frac{2}{3}$.</p>\n<p></p>", "stepsPenalty": "1", "marks": 0, "gaps": [{"answer": "{base4}^{prodpow4}", "marks": 1, "maxlength": {"partialCredit": 0, "length": "13", "message": "<p>Your answer is longer than it needs to be.</p>"}, "showpreview": true, "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? ^ ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $x^y$.');\n}\n"}}, "checkingaccuracy": "0.0000001", "variableReplacements": [], "expectedvariablenames": [], "musthave": {"strings": ["^"], "partialCredit": 0, "showStrings": false, "message": "<p>Use ^ for powers. Input your answer in index form.</p>"}, "answersimplification": "fractionNumbers", "vsetrange": [0, 1], "checkingtype": "absdiff", "variableReplacementStrategy": "originalfirst", "type": "jme", "vsetrangepoints": 5, "notallowed": {"strings": ["^0"], "partialCredit": 0, "showStrings": false, "message": "<p>Use ^ for powers. Input your answer in index form.</p>"}, "showCorrectAnswer": true, "checkvariablenames": false}], "steps": [{"prompt": "<p><em>Multiply all the powers together as you have done in previous questions.</em></p>\n<hr/>\n<p>Note the answer can be written using a fractional power or a decimal power but a fractional power is more commonly used.</p>", "marks": 0, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "information"}], "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "gapfill"}], "tags": ["exponent", "exponents", "index", "index laws", "Index Laws", "indices", "multiplying", "nested power", "power", "power of a power", "powers"], "showQuestionGroupNames": false, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"den": {"name": "den", "definition": "random(10,20,25)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "base4": {"name": "base4", "definition": "primes[1]", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "base1": {"name": "base1", "definition": "random(2,3,5,7)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "base3": {"name": "base3", "definition": "primes[0]", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "prodpow2": {"name": "prodpow2", "definition": "powers2[0][0]*powers2[1][0]", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "primes": {"name": "primes", "definition": "shuffle([11,13,17,19])[0..2] ", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "base2": {"name": "base2", "definition": "random([2,3,5,7] except base1)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "ndec": {"name": "ndec", "definition": "random(-0.9..-0.1#0.1)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "nint": {"name": "nint", "definition": "random(-12..-2)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "prodpow4": {"name": "prodpow4", "definition": "nint*ndec*num/den", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "num": {"name": "num", "definition": "random(-9..-1)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "powers2": {"name": "powers2", "definition": "shuffle([[3,\"three\"],[4,\"four\"],[5,\"five\"],[6,\"six\"]])[0..2]", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "prodpow3": {"name": "prodpow3", "definition": "powers3[0][0]*powers3[1][0]*powers3[2][0]", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "powers1": {"name": "powers1", "definition": "random(3..6)", "description": "<p>2..6</p>", "templateType": "anything", "group": "Ungrouped variables"}, "powers3": {"name": "powers3", "definition": "shuffle([[2,\"two\"],[3,\"three\"],[4,\"four\"],[5,\"five\"],[6,\"six\"]])[0..3]", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "prodpow1": {"name": "prodpow1", "definition": "2*powers1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}}, "ungrouped_variables": ["primes", "base1", "powers1", "prodpow1", "base2", "powers2", "prodpow2", "base3", "powers3", "prodpow3", "base4", "ndec", "nint", "num", "den", "prodpow4"], "question_groups": [{"name": "", "questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0}], "metadata": {"description": "", "notes": "<p>I had to use string length restrictions to stop students just writing the question.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}]}], "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}