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Simplify \(\sqrt[3]{(64r^6)^{\frac{1}{2}}}\)


Question

Simplify \(\sqrt[3]{(64r^6)^{\frac{1}{2}}}\)

Options

A) \(\frac{r}{2}\)

B) 2r

C) \(\frac{1}{2r}\)

D) \(\frac{2}{r}\)

E) 64r

The correct answer is E.

Explanation:

\(\sqrt[3]{(64r^6)^{\frac{1}{2}}}\)
\(= (64r^6)^{\frac{1}{2} \cdot \frac{1}{3}}\)
\(= 64r^{6 \cdot \frac{1}{6}}\)
\(= 64r\)

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