// Numbas version: finer_feedback_settings
{"name": "36.c Simplifying multiplication 3 - multiplying powers of one variable", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "36.c Simplifying multiplication 3 - multiplying powers of one variable", "tags": [], "metadata": {"description": "<p>Simplifying single term expressions involving indices.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify the following expression.</p>\n<p>{MultiplicationToSimplify}</p>", "advice": "<p>To simplify $\\var{expression(Termchoice[0]+\"*\"+Termchoice[1])}$ we need to multiply the coefficients together and multiply $\\var{expression(LetterPower1)}$ with $\\var{expression(LetterPower2)}$ because they are powers of the same variable. Multiplying the coefficients together gives us</p>\n<p>\\[\\var{Coefficient1}\\times\\var{Coefficient2}=\\simplify[all]{{expression(Coefficient1+\"*\"+Coefficient2)}}.\\]</p>\n<p>To multiply $\\var{expression(LetterPower1)}$ with $\\var{expression(LetterPower2)}$ we add the powers together to give us $\\simplify[all]{{expression(LetterPower1+\"*\"+LetterPower2)}}$. Putting these together we get a final simplified answer of&nbsp;</p>\n<p>\\[\\var{Answer}.\\]</p>\n<p></p>\n<p><a href=\"https://sheffield.ac.uk/mash/maths-resources/maths-all#Algebra\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"LetterList": {"name": "LetterList", "group": "Ungrouped variables", "definition": "[\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"]", "description": "", "templateType": "anything", "can_override": false}, "Letter1": {"name": "Letter1", "group": "Ungrouped variables", "definition": "random(LetterList)", "description": "", "templateType": "anything", "can_override": false}, "TermChoice": {"name": "TermChoice", "group": "Ungrouped variables", "definition": "[Coefficient1+LetterPower1,Coefficient2+LetterPower2]", "description": "", "templateType": "anything", "can_override": false}, "MultiplicationToSimplify": {"name": "MultiplicationToSimplify", "group": "Ungrouped variables", "definition": "\"<p>$\\\\var{expression(Termchoice[0]+\\\"*\\\"+Termchoice[1])}$</p>\"", "description": "", "templateType": "long string", "can_override": false}, "Answer": {"name": "Answer", "group": "Ungrouped variables", "definition": "simplify(expression(Termchoice[0]+\"*\"+Termchoice[1]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "Coefficient1": {"name": "Coefficient1", "group": "Ungrouped variables", "definition": "string(random(2..8))", "description": "", "templateType": "anything", "can_override": false}, "Coefficient2": {"name": "Coefficient2", "group": "Ungrouped variables", "definition": "string(random(2..8))", "description": "", "templateType": "anything", "can_override": false}, "Power1": {"name": "Power1", "group": "Ungrouped variables", "definition": "string(random(1..3))", "description": "", "templateType": "anything", "can_override": false}, "Power2": {"name": "Power2", "group": "Ungrouped variables", "definition": "string(random(1..3))", "description": "", "templateType": "anything", "can_override": false}, "LetterPower1": {"name": "LetterPower1", "group": "Ungrouped variables", "definition": "if(Power1=\"1\",Letter1,Letter1+\"^\"+Power1)", "description": "", "templateType": "anything", "can_override": false}, "LetterPower2": {"name": "LetterPower2", "group": "Ungrouped variables", "definition": "if(Power2=\"1\",Letter1,Letter1+\"^\"+Power2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "not(Power1=\"1\" && Power2=\"1\")", "maxRuns": 100}, "ungrouped_variables": ["LetterList", "Letter1", "Coefficient1", "Coefficient2", "Power1", "Power2", "LetterPower1", "LetterPower2", "TermChoice", "MultiplicationToSimplify", "Answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{Answer}", "answerSimplification": "!all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "$n*$v^$n", "partialCredit": 0, "message": "", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "resources": []}]}], "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}]}