Question

How do you evaluate ${(-1)}^{\frac{2}{3}}$?

Answer 1

Evaluate the required value:

Here, ${(-1)}^{\frac{2}{3}}$ $={\left\{{\left(-1\right)}^2\right\}}^{\frac{1}{3}}$ $\left[\because {\mathrm{a}}^{\mathrm{m}\times \mathrm{n}}={\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}\right]$

$={\left\{1\right\}}^{\frac{1}{3}}$

$=\sqrt[3]{1}$ $\left[\because {\mathrm{a}}^{\frac{1}{\mathrm{m}}}=\sqrt[\mathrm{m}]{\mathrm{a}}\right]$

$=1$

Hence, the value of ${(-1)}^{\frac{2}{3}}$ is $1$.