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Advanced Math / Equivalent expressions Difficulty: Medium

Which expression is equivalent to $RootIndex 7 StartRoot x Superscript 9 Baseline y Superscript 9 Baseline EndRoot$ , where $x$ and $y$ are positive?

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Explanation

Choice B is correct. For positive values of $a$ and $b$ , $a^{m} b^{m} = {(a b)}^{m}$ , $\sqrt[n]{a} = {(a)}^{\frac{1}{n}}$ , and ${(a^{j})}^{k} = a^{j k}$ . Therefore, the given expression, $RootIndex 7 StartRoot x Superscript 9 Baseline y Superscript 9 Baseline EndRoot$ , can be rewritten as $RootIndex 7 StartRoot left parenthesis x y right parenthesis Superscript 9 Baseline EndRoot$ . This expression is equivalent to $left parenthesis left parenthesis x y right parenthesis Superscript 9 Baseline right parenthesis Superscript one seventh$ , which can be rewritten as $left parenthesis x y right parenthesis Superscript 9 dot one seventh$ , or ${(x y)}^{\frac{9}{7}}$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.