// Numbas version: exam_results_page_options {"name": "Algebra IV: Properties of indices (3) - Negative integers/fractions", "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", "sar", "sar2", "sar3", "sar4"], "name": "Algebra IV: Properties of indices (3) - Negative integers/fractions", "tags": [], "preamble": {"css": "", "js": ""}, "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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• $x^0 = 1$
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• $x^\\frac{a}{b} = (\\sqrt[b]{x})^{a}$
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• $x^{\\simplify{-a/b}}$ = $\\frac{1}{(\\sqrt[b]{x})^{a}}$
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• $x^{-a} = \\frac{1}{x^{a}}$
• \n
", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "

$\\var{c}^{\\simplify{-1/{b}}}$

", "allowFractions": true, "variableReplacements": [], "maxValue": "1/2", "minValue": "1/2", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

This question can alternatively be considered as being :

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$a^{\\simplify{-1/b}}$ = $\\frac{1}{\\sqrt[b]{a}}$

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$\\var{d}^{\\simplify{-1/{a}}}$

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This question can alternatively be considered as being :

\n

$a^{\\simplify{-1/b}}$ = $\\frac{1}{\\sqrt[b]{a}}$

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$\\var{h}^{\\simplify{-{f}/{g}}}$

", "allowFractions": true, "variableReplacements": [], "maxValue": "3^-{f}", "minValue": "3^-{f}", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

This question can alternatively be considered as being :

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$a^{\\simplify{-c/b}}$ = $\\frac{1}{(\\sqrt[b]{a})^{c}}$

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$\\var{l}^{\\simplify{-{k}/{j}}}$

", "allowFractions": true, "variableReplacements": [], "maxValue": "2^-k", "minValue": "2^-k", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

This question can alternatively be considered as being :

\n

$a^{\\simplify{-c/b}}$ = $\\frac{1}{(\\sqrt[b]{a})^{c}}$

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$\\var{f3}^{\\simplify{-{f1}/{f2}}}$

", "allowFractions": true, "variableReplacements": [], "maxValue": "5^-f1", "minValue": "5^-f1", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

This question can alternatively be considered as being :

\n

$a^{\\simplify{-c/b}}$ = $\\frac{1}{(\\sqrt[b]{a})^{c}}$

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$(\\var{sar}/\\var{sar2})^{-2}$

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Firstly, you need to consider BODMAS and how this affects the above expression.

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Using laws of indices:

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

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$(\\var{sar3}/\\var{sar4})^{-4}$

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", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": true, "variableReplacements": [], "maxValue": "({sar3}/{sar4})^-4", "strictPrecision": false, "minValue": "({sar3}/{sar4})^-4", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

Firstly, you need to consider BODMAS and how this affects the above expression.

\n

Using laws of indices:

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

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Simplify the following questions, giving your answer in its simplest form (as a fraction - unless asked otherwise).

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Recall:

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• $x^{\\simplify{-a/b}}$ = $\\frac{1}{(\\sqrt[b]{x})^{a}}$
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• $x^{-a} = \\frac{1}{x^{a}}$
• \n
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You may need a calculator for some of the questions.

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Simplifying indices

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