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

Answer:

Explanation:

$\frac{1}{(216)^{-\frac{2}{3}}}$ $+\frac{1}{(256)^{-\frac{3}{4}}}$ $+\frac{1}{(32)^{-\frac{1}{5}}}$

$=\frac{1}{(6^{3})^{-\frac{2}{3}}}$ $+\frac{1}{(4^{4})^{\left(-\frac{3}{4}\right)}}$ $+\frac{1}{(2^{5})^{-\frac{1}{5}}}$

$=\frac{1}{6^{3} \times \frac{(-2)}{3}}$ $+\frac{1}{4^{4}\times \frac{(-3)}{4}}$ $+\frac{1}{2^{5} \times \frac{-1}{5}}$

$=\frac{1}{6^{-2}}$ $+\frac{1}{4^{-3}}$ $+\frac{1}{2^{-1}}$

$=6^{2}+4^{3}+2^{1}$

$=(36+64+2)=102$