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1. The value of $\frac{1}{{(216)}^{- \frac{2}{3}}} +$ $\frac{1}{{(256)}^{- \frac{3}{4}}} +$ $\frac{1}{{(32)}^{- \frac{1}{5}}}$ is = ?

A. 102

B. 105

C. 107

D. 109

Solution:

\begin{aligned} \frac{1}{{(216)}^{- \frac{2}{3}}} + \frac{1}{{(256)}^{- \frac{3}{4}}} + \frac{1}{{(32)}^{- \frac{1}{5}}} \\ = \frac{1}{{(6^{3})}^{- \frac{2}{3}}} + \frac{1}{{(4^{4})}^{- \frac{3}{4}}} + \frac{1}{{(2^{5})}^{- \frac{1}{5}}} \\ = \frac{1}{6^{3 \times \frac{(- 2)}{3}}} + \frac{1}{4^{4 \times \frac{(- 3)}{4}}} + \frac{1}{2^{5 \times \frac{(- 1)}{5}}} \\ = \frac{1}{6^{- 2}} + \frac{1}{4^{- 3}} + \frac{1}{2^{- 1}} \\ = (6^{2} + 4^{3} + 2^{1}) \\ = (36 + 64 + 2) \\ = 102 \end{aligned}

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