Question

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

Answer 1

Let

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

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

$=4\left(6^2\right)+1\left(4^3\right)+2\left(3\right)$

$a=144+64+6=214$

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