// Numbas version: exam_results_page_options
{"name": "Jinhua's copy of Indices 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "f1", "f2", "f3", "f4", "t1", "t2"], "name": "Jinhua's copy of Indices 1", "tags": [], "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');"}, "advice": "<p><em><strong>Recall the laws of indices to help solve these problems:</strong></em></p>\n<p>$x^a \\times x^b = x^{a+b}$</p>\n<p>$x^a \\div x^b = x^{a-b}$</p>\n<p>$x^{-a} = \\frac{1}{x^a}$</p>\n<p>$(x^a)^b = x^{ab}$</p>\n<p>$(\\frac{x}{y})^a = \\frac{x^a}{y^a}$</p>\n<p>$x^\\frac{a}{b} = \\sqrt[b]{x^a}$</p>\n<p>$x^0 = 1$</p>\n<p>&nbsp;</p>\n<p><em><strong>Worked Solutions:</strong></em></p>\n<p>When evaluating fractional indices, it's often a good idea to rearrange the notation into radical signs and integer powers.</p>\n<p>Part f), for example, would become.</p>\n<p>&nbsp;$49^{\\simplify{3/2}}=\\sqrt{49^3}$</p>\n<p>Once seen in this way, it becomes easier to see how&nbsp;the base can be simplified.</p>\n<p>$\\sqrt{49^3}=\\sqrt{49\\times49\\times49}=\\sqrt{49^2}\\times\\sqrt{49}=49\\sqrt{49}=49\\times7=343$</p>\n<p>&nbsp;</p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\var{c}^{\\frac{1}{\\var{b}}}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "2", "minValue": "2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{d}^{\\frac{1}{\\var{a}}}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "3", "minValue": "3", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{h}^\\frac{\\var{f}}{\\var{g}}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "3^{f}", "minValue": "3^{f}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{l}^\\frac{\\var{k}}{\\var{j}}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "2^k", "minValue": "2^k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{f3}^\\frac{\\var{f1}}{\\var{f2}}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "5^f1", "minValue": "5^f1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$49^{\\simplify{3/2}}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "343", "minValue": "343", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$(\\simplify{1/{f4}})^\\frac{\\var{f2}}{\\var{f1}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "5^-{f2}", "minValue": "5^-{f2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$(\\frac{\\var{t1}}{\\var{t2}})^{\\frac{\\var{f1}}{\\var{f2}}}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(2/3)^{f1}", "minValue": "(2/3)^{f1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>Simplify the following and find their final values (either an&nbsp;integer or a&nbsp;fraction).</p>\n<p><em><strong>Note:</strong> Look out for the fractions in either the base or the index which&nbsp;may be simplified before proceeding to evaluate. If you're unsure with the method involved, click 'Reveal answers' and study the Advice section. Once you feel comfortable with the theory, click 'Try another question like this one' to regenerate the exercises.</em></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "f1": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "c": {"definition": "2^b", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "f4": {"definition": "5^f1", "templateType": "anything", "group": "Ungrouped variables", "name": "f4", "description": ""}, "d": {"definition": "3^a", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(2..4 except f)", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "3^g", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(2..5 except j)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "t2": {"definition": "3^f2", "templateType": "anything", "group": "Ungrouped variables", "name": "t2", "description": ""}, "l": {"definition": "2^j", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "f2": {"definition": "random(2..4 except f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "t1": {"definition": "2^f2", "templateType": "anything", "group": "Ungrouped variables", "name": "t1", "description": ""}, "f3": {"definition": "5^f2", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}}, "metadata": {"description": "<p>Simplifying indices.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}