Question

$\sqrt[4]{{\left(81\right)}^{-2}}$ is equal to _________.

Answer 1

$$\begin{gathered} \sqrt[4]{{\left(81\right)}^{-2}}={\left\{{\left(81\right)}^{-2}\right\}}^{\frac{1}{4}} \\ ={\left(81\right)}^{-2\times \frac{1}{4}} \\ ={\left(81\right)}^{-\frac{1}{2}} \\ ={\left(3^4\right)}^{-\frac{1}{2}} \\ ={\left(3\right)}^{4\times \left(-\frac{1}{2}\right)} \\ ={\left(3\right)}^{-2} \\ =\frac{1}{3^2} \\ =\frac{1}{9} \end{gathered}$$

Hence, $\sqrt[4]{{\left(81\right)}^{-2}}$ is equal to $\underline{\frac{1}{9}}$.