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

$\displaystyle{{\left({512}{{m}}^{{12}}{n}\right)}}^{{\frac{{1}}{{3}}}}={{512}}^{{\frac{{1}}{{3}}}}\cdot{{m}}^{{\frac{{12}}{{3}}}}\cdot{{n}}^{{\frac{{1}}{{3}}}}\usepackage{cmbright}\Huge\$

Calculate the coefficient and simplify the exponents of the variables.