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1. The value of ${(0.03125)}^{- \frac{2}{5}}$ is = ?

A. 4

B. 9

C. 12

D. 31.25

Solution:

\begin{aligned} {(0.03125)}^{- \frac{2}{5}} \\ = {[{(0.5)}^{5}]}^{- \frac{2}{5}} \\ = {0.5}^{[5 \times (- \frac{2}{5})]} \\ = {(0.5)}^{- 2} \\ = \frac{1}{{(0.5)}^{2}} \\ = \frac{1}{0.25} \\ = 4 \end{aligned}

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