Question

Simplify $\frac{4}{{\left(216\right)}^{-2/3}}+\frac{1}{{\left(256\right)}^{-3/4}}+\frac{2}{{\left(243\right)}^{-1/5}}$

Answer 1

$\frac{4}{{\left(216\right)}^{-2/3}}+\frac{1}{{\left(256\right)}^{-3/4}}+\frac{2}{{\left(243\right)}^{-1/5}}$
$=\frac{4}{{\left(6^3\right)}^{-2/3}}+\frac{1}{{\left(4^4\right)}^{-3/4}}+\frac{2}{{\left(3^5\right)}^{-1/5}}$
$=\frac{4}{6^{-2}}+\frac{1}{4^{-3}}+\frac{2}{3^{-1}}$
$=(4\times 6^2)+\left(4^3\right)+(2\times 3)$
$=(4\times 36)+64+6$
$=144+70$
$=214$

Hence, $\frac{4}{{\left(216\right)}^{-2/3}}+\frac{1}{{\left(256\right)}^{-3/4}}+\frac{2}{{\left(243\right)}^{-1/5}}=214$