Question

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

• A. 102
• B. 105
• C. 107
• D. 111

Answer 1

The correct option is A

102

$\begin{array}{c}\frac{1}{{\left(216\right)}^{-\frac{2}{3}}}+\frac{1}{{\left(256\right)}^{-\frac{3}{4}}}+\frac{1}{{\left(32\right)}^{-\frac{1}{5}}}=\frac{1}{{\left(6^3\right)}^{-\frac{2}{3}}}+\frac{1}{{\left(4^4\right)}^{-\frac{3}{4}}}+\frac{1}{{\left(2^5\right)}^{-\frac{1}{5}}}\\ =\frac{1}{6^3{\times }^{\frac{\left(-2\right)}{3}}}+\frac{1}{\left(4^4\right){\times }^{\frac{\left(-3\right)}{4}}}+\frac{1}{\left(2^5\right){\times }^{\frac{\left(-1\right)}{5}}}\\ =\frac{1}{6^{-2}}+\frac{1}{4^{-3}}+\frac{1}{2^{-1}}\\ =\left(6^2+4^3+2^1\right)=\left(36+64+2\right)=102.\end{array}$