Simplify

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

$=\left\{(256)^{-\frac{1}{2}}\right\}^{\frac{1}{2}}$

$=(256)^{-\frac{1}{4}}$

$=\left(4^{4}\right)^{-\frac{1}{4}}$

$=4^{-1}$

$=\frac{1}{4}$