Rewrite the radical using a rational exponent: $\displaystyle{{\left({9}{{m}}^{{2}}{{n}}^{{16}}\right)}}^{{\frac{{1}}{{4}}}}\usepackage{cmbright}\Huge\$

Use the laws of exponents to simplify: $\displaystyle{{9}}^{{\frac{{1}}{{4}}}}\cdot{{m}}^{{\frac{{2}}{{4}}}}\cdot{{n}}^{{\frac{{16}}{{4}}}}\usepackage{cmbright}\Huge\$

Factor 9 and simplify: $\displaystyle{{\left({3}\cdot{3}\right)}}^{{\frac{{1}}{{4}}}}\cdot{{m}}^{{\frac{{1}}{{2}}}}\cdot{{n}}^{{4}}={{\left({{3}}^{{2}}\right)}}^{{\frac{{1}}{{4}}}}\cdot{{m}}^{{\frac{{1}}{{2}}}}\cdot{{n}}^{{4}}={{3}}^{{\frac{{1}}{{2}}}}{{m}}^{{\frac{{1}}{{2}}}}{{n}}^{{4}}\usepackage{cmbright}\Huge\$

Change the factors with exponent $\displaystyle\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ back to radical form: $\displaystyle{{n}}^{{4}}\sqrt{{{3}{m}}}\usepackage{cmbright}\Huge\$