Question

Simplify ${\left[{\left\{{\left(256\right)}^{-\frac{1}{2}}\right\}}^{\frac{1}{4}}\right]}^2$.

Answer 1

$$\begin{gathered} {\left[{\left\{{\left(256\right)}^{-\frac{1}{2}}\right\}}^{\frac{1}{4}}\right]}^2 \\ ={\left\{{\left(256\right)}^{-\frac{1}{2}}\right\}}^{\frac{1}{2}} \\ ={\left(256\right)}^{-\frac{1}{4}} \\ ={\left(4^4\right)}^{-\frac{1}{4}} \\ =4^{-1} \\ =\frac{1}{4} \end{gathered}$$