You applied the rational exponent only to the coefficient of the expression. However, correctly applying the rules of exponents would give you:

$\displaystyle{{\left({256}{{x}}^{{16}}{{y}}^{{2}}\right)}}^{{\frac{{1}}{{4}}}}={{256}}^{{\frac{{1}}{{4}}}}\cdot{{x}}^{{\frac{{16}}{{4}}}}\cdot{{y}}^{{\frac{{2}}{{4}}}}\usepackage{cmbright}\Huge\$

In addition to calculating the coefficient, simplify the exponents of the variables.