Question

How do you simplify ${\left(125\right)}^{-\frac{1}{3}}$?

Answer 1

Simplify the given number:

The given irrational number is ${\left(125\right)}^{-\frac{1}{3}}$.

$\therefore {\left(125\right)}^{-\frac{1}{3}}={\left(5\times 5\times 5\right)}^{-\frac{1}{3}}$

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

$=5^{-1}$ $.\mathbf{.}\mathbf{.}\left[\because {\left(a^m\right)}^n=a^{mn}\right]$

$=\frac{1}{5}$

Hence, the simplified value of ${\left(125\right)}^{-\frac{1}{3}}$ is $\frac{1}{5}$.