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Evaluate \(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\time...

Evaluate $\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}$

A.

¹/₃

B.

3

C.

6

D.

¹/₆

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Correct answer is A

$\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}=\frac{1}{\left(\frac{81}{16}\right)^{\frac{1}{4}}}\times \frac{1}{2}\\ =\left(\frac{16}{81}\right)^{\frac{1}{4}}\times \frac{1}{2}\\ =\left(\frac{2}{3}\right)^{4\times \frac{1}{4}}\\ =\frac{2}{3}\times \frac{1}{2}\\ =\frac{1}{3}$

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