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1. Simplified from of ${[{(\sqrt[5]{x^{- \frac{3}{5}}})}^{- \frac{5}{3}}]}^{5}$ is = ?

A. $\frac{1}{x}$

B. x

C. x^-5

D. x⁵

Solution:

\begin{aligned} {[{(\sqrt[5]{x^{- \frac{3}{5}}})}^{- \frac{5}{3}}]}^{5} \\ = {[{{(x^{- \frac{3}{5}})}^{\frac{1}{5}}}^{- \frac{5}{3}}]}^{5} \\ = {[{(x^{^{{(- \frac{3}{5}) \times \frac{1}{5}}}})}^{- \frac{5}{3}}]}^{5} \\ = {[{(x^{- \frac{3}{25}})}^{- \frac{5}{3}}]}^{5} \\ = {[x^{{(- \frac{3}{25}) \times (- \frac{5}{3})}}]}^{5} \\ = {(x^{\frac{1}{5}})}^{5} \\ = x^{(\frac{1}{5} \times 5)} \\ = x \end{aligned}

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