// Numbas version: exam_results_page_options
{"name": "Calculating powers (-a^(-a))", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>This question tests a student's ability to raise a positive base to a negative exponent and then take the negative. The base and the exponent have the same absolute value.</p>"}, "variables": {"a": {"definition": "random(2..7)", "templateType": "anything", "description": "<p>This is the base and the absolute value of the exponent.</p>", "group": "Ungrouped variables", "name": "a"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "rulesets": {"std": ["all"]}, "variable_groups": [], "preamble": {"js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');", "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"}, "tags": [], "advice": "<p>The correct calculation is $-\\var{a}^{-\\var{a}}=-\\dfrac{1}{\\var{a}^\\var{a}}=-\\dfrac{1}{\\var{a^a}}=\\dfrac{1}{\\boxed{\\var{-a^a}}}$.</p>\n<p><span data-jme-visible=\"mod(a,2)=0\">Remember that the minus sign is not raised to the power, so even though $-\\var{a}$ that is the exponent is even, $-\\var{a}^{\\var{-a}}$ is negative.</span></p>", "functions": {}, "parts": [{"scripts": {}, "variableReplacements": [], "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>$-\\var{a}^{-\\var{a}}=\\ $ <fraction><numerator>1</numerator><denominator>[[0]]</denominator></fraction>.</p>", "gaps": [{"mustBeReducedPC": 0, "minValue": "-a^a", "variableReplacementStrategy": "originalfirst", "maxValue": "-a^a", "correctAnswerFraction": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain", "variableReplacements": []}], "type": "gapfill"}], "ungrouped_variables": ["a"], "statement": "<p>Calculate the following power.</p>\n<p>If you think the answer should be negative then a negative sign should be entered in the denominator.</p>\n<p></p>", "name": "Calculating powers (-a^(-a))", "type": "question", "contributors": [{"name": "Anthony Brown", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/799/"}]}]}], "contributors": [{"name": "Anthony Brown", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/799/"}]}