Correct. Using the power property: $\displaystyle{\log}_{{b}}{{M}}^{{n}}={n}\cdot{\log}_{{b}}{M}\usepackage{cmbright}\Huge\$

This gives you $\displaystyle{\log}_{{{20}}}{{400}}^{{8}}={8}\cdot{\log}_{{{20}}}{400}\usepackage{cmbright}\Huge\$ .

You can rewrite 400 as $\displaystyle{{20}}^{{2}}\usepackage{cmbright}\Huge\$ , so $\displaystyle{\log}_{{{20}}}{400}={2}\usepackage{cmbright}\Huge\$ .

Therefore, $\displaystyle{\log}_{{{20}}}{{400}}^{{8}}={8}\cdot{2}={16}\usepackage{cmbright}\Huge\$ .