Question

Simplify ${\left(\frac{64}{125}\right)}^{\frac{-2}{3}}$

Answer 1

Consider the given expression,

$\Rightarrow {\left(\frac{64}{125}\right)}^{\frac{-2}{3}}={\left(\frac{125}{64}\right)}^{\frac{2}{3}}$

$={\left(\frac{5^3}{4^3}\right)}^{\frac{2}{3}}={\left(\frac{5}{4}\right)}^{\frac{3\times 2}{3}}$

$={\left(\frac{5}{4}\right)}^2=\frac{25}{16}$

$\Rightarrow {\left(\frac{64}{125}\right)}^{\frac{-2}{3}}=\frac{25}{16}$

Hence, this is the answer.