Question

The value of $\sqrt[4]{{\left(64\right)}^{-2}}$ is

(a) $\frac{1}{8}$

(b) $\frac{1}{2}$

(c) 8

(d) $\frac{1}{64}$

Answer 1

$$\begin{gathered} \sqrt[4]{{\left(64\right)}^{-2}}={\left[{\left(64\right)}^{-2}\right]}^{\frac{1}{4}} \\ ={\left[{\left(2^6\right)}^{-2}\right]}^{\frac{1}{4}} \\ ={\left[2^{-12}\right]}^{\frac{1}{4}} \\ =2^{-3} \\ =\frac{1}{2^3} \\ =\frac{1}{8} \end{gathered}$$

$\therefore$ The value of $\sqrt[4]{{\left(64\right)}^{-2}}$ is $\frac{1}{8}$.

Hence, the correct option is (a).