Simplify and express the result in its simplest form
$\sqrt[3]{24} \div (\sqrt[4]{2} \cdot \sqrt[3]{3})$

\sqrt[12]{512}

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\sqrt[12]{502}

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\sqrt[12]{256}

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\sqrt[6]{512}

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Solution

The correct option is A $\sqrt[12]{512}$
$\sqrt[3]{24} \div (\sqrt[4]{2} \cdot \sqrt[3]{3})$

$= 24^{\frac{1}{3}} \div (2^{\frac{1}{4}} \cdot 3^{\frac{1}{3}})$

$= 24^{\frac{1 \times 4}{3 \times 4}} \div (2^{\frac{1 \times 3}{4 \times 3}} \cdot 3^{\frac{1 \times 4}{3 \times 4}})$

$= \sqrt[12]{331776 \div 8 \cdot 81}$

$= \sqrt[12]{512}$

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