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{"name": "Maria's copy of Algebra IV: Properties of indices (2) - Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>Simplify the following expressions, giving your answer in its simplest form.</p>\n<p>Give your answer as either a fraction or an integer.</p>\n<p></p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Simplifying indices.</p>"}, "variable_groups": [], "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "f1", "f2", "f3", "f4", "t1", "t2"], "advice": "<p>Recall the laws of indices:</p>\n<p>$x^a \\times x^b = x^{a+b}$<br/>$x^a \\div x^b = x^{a-b}$<br/>$x^{-a} = \\frac{1}{x^a}$<br/>$(x^a)^b = x^{ab}$<br/>$(\\frac{x}{y})^a = \\frac{x^a}{y^a}$<br/>$x^\\frac{a}{b} = (\\sqrt[b]{x})^{a}$<br/>$x^0 = 1$</p>", "extensions": [], "rulesets": {}, "preamble": {"css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n\n", "js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');"}, "name": "Maria's copy of Algebra IV: Properties of indices (2) - Fractions", "parts": [{"showCorrectAnswer": true, "marks": 1, "scripts": {}, "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "minValue": "2", "useCustomName": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "prompt": "<p>$\\var{c}^{\\frac{1}{\\var{b}}}$</p>", "unitTests": [], "showFractionHint": true, "steps": [{"showCorrectAnswer": true, "unitTests": [], "marks": 0, "scripts": {}, "customName": "", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "showFeedbackIcon": true, "variableReplacements": [], "type": "information", "extendBaseMarkingAlgorithm": true, "prompt": "<p>Hint: $x^{1/z}$ is the same as $\\sqrt[z]{x}$</p>", "customMarkingAlgorithm": ""}], "stepsPenalty": 0, "allowFractions": false, "customName": "", "maxValue": "2", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "type": "numberentry", "correctAnswerStyle": "plain", "customMarkingAlgorithm": ""}], "functions": {}, "variables": {"c": {"name": "c", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "2^b"}, "h": {"name": "h", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "3^g"}, "d": {"name": "d", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "3^a"}, "f2": {"name": "f2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(3..6)"}, "k": {"name": "k", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..5 except j)"}, "f": {"name": "f", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..g-1)"}, "g": {"name": "g", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(3..6)"}, "f3": {"name": "f3", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "5^f2"}, "a": {"name": "a", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..5)"}, "l": {"name": "l", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "2^j"}, "f1": {"name": "f1", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..f2-1)"}, "t1": {"name": "t1", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "2^f2"}, "b": {"name": "b", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..3)"}, "t2": {"name": "t2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "3^f2"}, "f4": {"name": "f4", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "5^f1"}, "j": {"name": "j", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..5)"}}, "type": "question", "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}