Question

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

Answer 1

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

Using the property

$\frac{1}{x^{-n}}=x^n$

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

Substitute $216=6^3$

$243=3^5$

$256=4^4$

$=2\times 6^{3\times \frac{2}{3}}-4\times 3^{5\times \frac{1}{5}}+1\times 4^{4\times \frac{3}{4}}$

$=2\times 6^2-4\times 3+1\times 4^3$

$=72-12+64$

$=124$.