Rewrite the radical using a rational exponent. The root, 8, determines the denominator of the fraction, so $\displaystyle\frac{{1}}{{8}}\usepackage{cmbright}\Huge\$ will be the rational exponent. Use a grouping symbol to show that the entire expression under the radical will be raised to the one-eighth power.

$\displaystyle{\sqrt[{{8}}]{{{256}{z}}}}={{\left({256}{z}\right)}}^{{\frac{{1}}{{8}}}}\usepackage{cmbright}\Huge\$