Question

Simplify:

${\left(\frac{625}{256}\right)}^{-\frac{3}{4}}$.

Answer 1

Now,

Let $a={\left(\frac{625}{256}\right)}^{-\frac{3}{4}}$

$={\left(\frac{5^4}{4^4}\right)}^{-\frac{3}{4}}$

$={\left(\frac{5}{4}\right)}^{-3}$

$={\left(\frac{4}{5}\right)}^3$

$a=\frac{64}{125}$.

$\therefore {\left(\frac{625}{256}\right)}^{-\frac{3}{4}}=\frac{64}{125}$