(24)1/2(200)1/3=(24)3/6(200)2/6=(243)1/6(2002)1/6=[24×24×24200×200]1/6=[216625]1/6

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$\sqrt{24} \div \sqrt[3]{200} =$

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${[\frac{216}{625}]}^{1 / 6}$

${[\frac{625}{216}]}^{1 / 6}$

${[\frac{24}{200}]}^{1 / 6}$

${[\frac{24}{200}]}^{1 / 3}$

answer is A.

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Detailed Solution

$\frac{{(24)}^{1 / 2}}{{(200)}^{1 / 3}} = \frac{{(24)}^{3 / 6}}{{(200)}^{2 / 6}}$

$= \frac{{(24^{3})}^{1 / 6}}{{(200^{2})}^{1 / 6}}$

$= {[\frac{24 \times 24 \times 24}{200 \times 200}]}^{1 / 6}$

$= {[\frac{216}{625}]}^{1 / 6}$

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