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1. ${(64)}^{- \frac{2}{3}} \times {(\frac{1}{4})}^{- 2}$ is equal to ?

A. 1

B. 2

C. $\frac{1}{2}$

D. $\frac{1}{16}$

Solution:

\begin{aligned} 6 4^{- \frac{2}{3}} \times {(\frac{1}{4})}^{- 2} \\ = {(4^{3})}^{- \frac{2}{3}} \times {(\frac{1}{4})}^{- 2} \\ = 4^{- 2} \times {(\frac{1}{4})}^{- 2} \\ = {(\frac{1}{4})}^{2} \times {(\frac{1}{4})}^{- 2} \\ = {(\frac{1}{4})}^{2 - 2} \\ = {(\frac{1}{4})}^{0} \\ = 1 \end{aligned}

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