Question

Find the value of $216$ to the power of $\frac{-2}{3}$

Answer 1

Compute the required value

We know that, $216=6^3$

$$\begin{gathered} \therefore {\left(216\right)}^{\frac{-2}{3}}={\left(6^3\right)}^{\frac{-2}{3}} \\ ={\left(6\right)}^{3\times \frac{-2}{3}}\left[\because {\left(a^m\right)}^n=a^{m\times n}\right] \\ =6^{-2} \\ =\frac{1}{6^2}\left[\because a^{-m}=\frac{1}{a^m}\right] \\ \Rightarrow {\left(216\right)}^{\frac{-2}{3}}=\frac{1}{36} \end{gathered}$$

Hence, the value of ${\left(216\right)}^{\frac{-2}{3}}$ is $\frac{1}{36}$