Correct. Apply the exponent 4 to each factor individually: $\displaystyle\frac{{{{4}}^{{4}}{{\left({{g}}^{{6}}\right)}}^{{4}}{{\left({{h}}^{{2}}\right)}}^{{4}}}}{{{{f}}^{{4}}{{\left({{g}}^{{2}}\right)}}^{{4}}}}\usepackage{cmbright}\Huge\$

Calculate $\displaystyle{{4}}^{{4}}\usepackage{cmbright}\Huge\$ and use the Power Rule: $\displaystyle\frac{{{256}{{g}}^{{{6}\cdot{4}}}{{h}}^{{{2}\cdot{4}}}}}{{{{f}}^{{4}}{{g}}^{{{2}\cdot{4}}}}}=\frac{{{256}{{g}}^{{24}}{{h}}^{{8}}}}{{{{f}}^{{4}}{{g}}^{{8}}}}\usepackage{cmbright}\Huge\$

Use the Quotient Rule: $\displaystyle\frac{{{256}{{g}}^{{{\left({24}-{8}\right)}}}{{h}}^{{{8}}}}}{{{f}}^{{4}}}=\frac{{{256}{{g}}^{{16}}{{h}}^{{8}}}}{{{f}}^{{4}}}\usepackage{cmbright}\Huge\$