[102] The value of \dfrac{1}{(216)^{-\dfrac{2}{3}}} +\dfrac{1}{(256)^{-\dfrac{3}{4}}} +\dfrac{1}{(32

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

102

105

107

109

Explanation:

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

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

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

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

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

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

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