Question

$\sqrt[4]{{\left(64\right)}^{-2}}=?$
(a) 4
(b) $\frac{1}{4}$
(c) 8
(d) $\frac{1}{8}$

Answer 1

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

We have:
$$\begin{gathered} \sqrt[4]{{\left(64\right)}^{-2}} \\ ={\left({\left(2\right)}^6\right)}^{\raisebox{1ex}{$-2$}\!\left/ \!\raisebox{-1ex}{$4$}\right.} \\ ={\left(2\right)}^{\raisebox{1ex}{$-12$}\!\left/ \!\raisebox{-1ex}{$4$}\right.} \\ ={\left(2\right)}^{-3} \\ ={\left(\frac{1}{2}\right)}^3 \\ =\frac{1}{8} \end{gathered}$$