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1. The value of ${(\frac{32}{243})}^{- \frac{4}{5}}$ is = ?

A. $\frac{4}{9}$

B. $\frac{9}{4}$

C. $\frac{16}{81}$

D. $\frac{81}{16}$

Solution:

\begin{aligned} {(\frac{32}{243})}^{- \frac{4}{5}} \\ = {{(\frac{2}{3})}^{5}}^{- \frac{4}{5}} \\ = {(\frac{2}{3})}^{5 \times \frac{(- 4)}{5}} \\ = {(\frac{2}{3})}^{(- 4)} \\ = {(\frac{3}{2})}^{4} \\ = \frac{3^{4}}{2^{4}} \\ = \frac{81}{16} \end{aligned}

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