Question

Find the value of ${\left(64\right)}^{\frac{-2}{3}}$

Answer 1

Compute the required value

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

We know that , $64=4^3$

$$\begin{gathered} \therefore {\left(64\right)}^{\frac{-2}{3}}={\left(4^3\right)}^{\frac{-2}{3}} \\ ={\left(4\right)}^{3\times \frac{-2}{3}}\mathbf{}\left[\because {\left(a^m\right)}^n=a^{m\times n}\right] \\ =4^{-2} \\ =\frac{1}{4^2}\mathbf{}\left[\because a^{-m}=\frac{1}{a^m}\right] \\ \Rightarrow {\left(64\right)}^{\frac{-2}{3}}=\frac{1}{16} \end{gathered}$$

Hence, the value of ${\left(64\right)}^{\frac{-2}{3}}$ is $\frac{1}{16}$