// Numbas version: exam_results_page_options {"name": "Indices 3", "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"], "name": "Indices 3", "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}", "js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');"}, "advice": "

Recall the laws of indices to help solve the problems:

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$x^a \\times x^b = x^{a+b}$

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$x^a \\div x^b = x^{a-b}$

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$x^{-a} = \\frac{1}{x^a}$

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$(x^a)^b = x^{ab}$

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$(\\frac{x}{y})^a = \\frac{x^a}{y^a}$

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$x^\\frac{a}{b} = \\sqrt[b]{x^a}$

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$x^0 = 1$

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$x^\\var{a} \\times x^\\var{b}$

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$p^\\var{c} \\times p^\\var{d}$

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$(\\var{a}k^\\var{b})^\\var{f}$

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$y^{1/\\var{a}} \\times y^{1/\\var{b}}$

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$c^\\var{a}$$c^\\var{b}$

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$\\var{a}h^\\var{c}$$\\var{b}h^\\var{d}$

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$(4d)^\\var{g}$$(2d)^\\var{h}$

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$(6p^{-\\var{f}})^{\\var{g}}$$(9p^{-\\var{j}})^{\\var{h}}$

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Simplify each of these, give your answer in simplest form.

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Simplifying indices

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