Question

Find the value of following
${\left(625\right)}^{\frac{-3}{4}}$

Answer 1

Let $a=(625{)}^{-3/4}$

$={\left(\frac{1}{625}\right)}^{3/4}$

$={\left(\sqrt[4]{4\frac{1}{5\times 5\times 5\times 5}}\right)}^3$

$={\left(\frac{1}{5}\right)}^3$

$a=\frac{1}{125}$.

$\therefore (625{)}^{-3/4}=\frac{1}{125}$