Please complete the following.
", "variable_groups": [{"variables": ["intpower", "intrhs", "intsoln"], "name": "a"}, {"variables": ["bpower", "bnice", "bsoln", "bxcoeff", "bb", "bc"], "name": "b"}], "ungrouped_variables": ["dpower", "dc", "db", "ddenom"], "variables": {"bxcoeff": {"group": "b", "description": "", "definition": "random(-3..3 except 0..1)", "name": "bxcoeff", "templateType": "anything"}, "bsoln": {"group": "b", "description": "", "definition": "bnice^bpower", "name": "bsoln", "templateType": "anything"}, "bnice": {"group": "b", "description": "((bc-bb)/bxcoeff)^(1/bpower)
", "definition": "switch(bpower=3 or bpower=2, random(-10..10 except -1..1), bpower=5 or bpower =4, random(-4..4 except -1..1), bpower=7 or bpower=6, random(-3..3 except -1..1), 2)", "name": "bnice", "templateType": "anything"}, "intpower": {"group": "a", "description": "", "definition": "random(2..9)", "name": "intpower", "templateType": "anything"}, "intrhs": {"group": "a", "description": "intsoln^intpower
", "definition": "switch(intpower=3 or intpower=4, random(2..12), intpower=5 or intpower=6, random(2..5), intpower=7 or intpower=8, random(2..3), 2)\n", "name": "intrhs", "templateType": "anything"}, "bpower": {"group": "b", "description": "", "definition": "random(2..9)", "name": "bpower", "templateType": "anything"}, "intsoln": {"group": "a", "description": "", "definition": "intrhs^intpower", "name": "intsoln", "templateType": "anything"}, "db": {"group": "Ungrouped variables", "description": "", "definition": "random(-100..100 except -1..1)", "name": "db", "templateType": "anything"}, "dc": {"group": "Ungrouped variables", "description": "", "definition": "random(-100..100 except -1..1)", "name": "dc", "templateType": "anything"}, "bc": {"group": "b", "description": "", "definition": "bnice*bxcoeff+bb", "name": "bc", "templateType": "anything"}, "bb": {"group": "b", "description": "", "definition": "random(1..100)", "name": "bb", "templateType": "anything"}, "ddenom": {"group": "Ungrouped variables", "description": "", "definition": "random(2..15)", "name": "ddenom", "templateType": "anything"}, "dpower": {"group": "Ungrouped variables", "description": "", "definition": "random(2..9)", "name": "dpower", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them).
"}, "parts": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "customName": "", "prompt": "If $\\sqrt[\\var{intpower}]{x}=\\var{intrhs}$, then $x=$ [[0]].
", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 1, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "customName": "", "answer": "{intsoln}", "showCorrectAnswer": true, "checkingAccuracy": 0.001, "checkVariableNames": false, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "type": "jme", "vsetRange": [0, 1], "useCustomName": false, "showFeedbackIcon": true, "showPreview": true, "valuegenerators": [], "variableReplacements": [], "scripts": {}}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "customName": "", "prompt": "If $\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}=\\var{bc}$, then $y=$ [[0]].
", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 1, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "customName": "", "answer": "{bsoln}", "showCorrectAnswer": true, "checkingAccuracy": 0.001, "checkVariableNames": false, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "type": "jme", "vsetRange": [0, 1], "useCustomName": false, "showFeedbackIcon": true, "showPreview": true, "valuegenerators": [], "variableReplacements": [], "scripts": {}}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "customName": "", "prompt": "For this question, if the answer was $\\left(\\frac{35}{11}\\right)^{11}-24$, then you could enter (35/11)^(11)-24.
\nIf $\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}=\\var{dc}$, then $z=$ [[0]].
", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "answerSimplification": "basic", "checkingType": "absdiff", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "customMarkingAlgorithm": "", "valuegenerators": [], "variableReplacements": [], "scripts": {}, "checkVariableNames": false, "failureRate": 1, "marks": 1, "unitTests": [], "customName": "", "answer": "({dc*ddenom})^({dpower})-{db}", "showCorrectAnswer": true, "vsetRangePoints": 5, "checkingAccuracy": 0.001, "extendBaseMarkingAlgorithm": true, "showPreview": true}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}}], "advice": "a) Given $\\sqrt[\\var{intpower}]{x}=\\var{intrhs}$, we raise both sides to the power of $\\var{intpower}$ to get $x$ by itself.
\n| $\\sqrt[\\var{intpower}]{x}$ | \n$=$ | \n$\\var{intrhs}$ | \n
| \n | \n | \n |
| $\\left(\\sqrt[\\var{intpower}]{x}\\right)^{\\var{intpower}}$ | \n$=$ | \n$\\simplify[basic]{({intrhs})^{intpower}}$ | \n
| \n | \n | \n |
| $x$ | \n$=$ | \n$\\var{intsoln}$ | \n
b) Given $\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}=\\var{bc}$, we can rearrange the equation to get $y^\\frac{1}{\\var{bpower}}$ by itself and then we can raise both sides to the power of $\\var{bpower}$ to get $y$ by itself.
\n| $\\simplify{{bxcoeff}y^(1/{bpower})+{bb}}$ | \n$=$ | \n$\\var{bc}$ | \n
| \n | \n | \n |
| $\\simplify{{bxcoeff}y^(1/{bpower})}$ | \n$=$ | \n$\\simplify[basic]{{bc}-{bb}}$ | \n
| \n | \n | \n |
| $\\simplify{{bxcoeff}y^(1/{bpower})}$ | \n$=$ | \n$\\simplify{{bc-bb}}$ | \n
| \n | \n | \n |
| $y^\\frac{1}{\\var{bpower}}$ | \n$=$ | \n$\\simplify[!basic]{{bc-bb}/{bxcoeff}}$ | \n
| \n | \n | \n |
| $y^\\frac{1}{\\var{bpower}}$ | \n$=$ | \n$\\simplify{{bc-bb}/{bxcoeff}}$ | \n
| \n | \n | \n |
| $\\left(y^\\frac{1}{\\var{bpower}}\\right)^{\\var{bpower}}$ | \n$=$ | \n$\\simplify[basic]{({(bc-bb)/bxcoeff})^{bpower}}$ | \n
| \n | \n | \n |
| $y$ | \n$=$ | \n$\\var{bsoln}$ | \n
c) Given $\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}=\\var{dc}$, we can rearrange the equation to get $\\simplify{(root(z+{db},{dpower}))}$ by itself, then we can raise both sides to the power of $\\var{dpower}$, and finally rearrange to get $z$ by itself.
\n| $\\displaystyle{\\simplify{(root(z+{db},{dpower}))/{ddenom}}}$ | \n$=$ | \n$\\var{dc}$ | \n
| \n | \n | \n |
| $\\displaystyle{\\simplify{(root(z+{db},{dpower}))}}$ | \n$=$ | \n$\\simplify[basic]{{dc}*{ddenom}}$ | \n
| \n | \n | \n |
| $\\displaystyle{\\simplify{(root(z+{db},{dpower}))}}$ | \n$=$ | \n$\\var{dc*ddenom}$ | \n
| \n | \n | \n |
| $\\left(\\sqrt[\\var{dpower}]{\\simplify{z+{db}}}\\right)^\\var{dpower}$ | \n$=$ | \n$\\simplify[basic]{({dc*ddenom})^{dpower}}$ | \n
| \n | \n | \n |
| $\\simplify{z+{db}}$ | \n$=$ | \n$\\simplify[basic]{-{abs(dc*ddenom)}^{dpower}}$ $\\simplify[basic]{({abs(dc*ddenom)})^{dpower}}$ $\\simplify[basic]{({(dc*ddenom)})^{dpower}}$ | \n
| \n | \n | \n |
| $z$ | \n$=$ | \n$\\simplify[basic]{-{abs(dc*ddenom)}^{dpower}-{db}}$ $\\simplify[basic]{({abs(dc*ddenom)})^{dpower}-{db}}$ $\\simplify[basic]{({(dc*ddenom)})^{dpower}-{db}}$ | \n