Question

Find the value of $\frac{4}{(216{)}^{-\frac{2}{3}}}+\frac{1}{(256{)}^{-\frac{3}{4}}}+\frac{2}{(243{)}^{-\frac{1}{5}}}$.

Answer 1

$(216{)}^{-\frac{2}{3}}=(6^3{)}^{-\frac{2}{3}}=6^{-2}=\frac{1}{36}$

$(256{)}^{-\frac{3}{4}}=(4^4{)}^{-\frac{3}{4}}=4^{-3}=\frac{1}{64}$

$(243{)}^{\frac{-1}{5}}=(3^5{)}^{-\frac{1}{5}}=3^{-1}=\frac{1}{3}$

$\frac{4}{(216{)}^{\frac{-2}{3}}}+\frac{1}{(256{)}^{\frac{-3}{4}}}+\frac{2}{(243{)}^{\frac{-1}{5}}}=\frac{4}{\frac{1}{36}}+\frac{1}{\frac{1}{64}}+\frac{2}{\frac{1}{3}}=4\times 36+64+2\times 3=144+64+6=214$