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

We have,
$\frac{4}{(216{)}^{-\frac{2}{3}}}+\frac{1}{(256{)}^{-\frac{3}{4}}}+\frac{2}{(243{)}^{-\frac{1}{5}}}$

$=\frac{4}{(6^3{)}^{-\frac{2}{3}}}+\frac{1}{({16}^2{)}^{-\frac{3}{4}}}+\frac{2}{(3^5{)}^{-\frac{1}{5}}}[\because 216=6^3,256={16}^2,243=3^5]=\frac{4}{6^{3\times (-\frac{2}{3})}}+\frac{1}{{16}^{2\times (-\frac{3}{4})}}+\frac{2}{3^{5\times (-\frac{1}{5})}}[\because (a^m{)}^n=a^{mn}]=\frac{4}{6^{-2}}+\frac{1}{{16}^{-\frac{3}{2}}}+\frac{2}{3^{-1}}=4\times 6^2+{16}^{\frac{3}{2}}+2\times 3^1[\because \frac{1}{a}=a^{-1}]=4\times 36+((4{)}^2{)}^{3/2}+2\times 3^1=4\times 36+4^3+6=144+64+6=214$