You forgot to take the absolute values of $\displaystyle{{f}}^{{3}}\usepackage{cmbright}\Huge\$ and $\displaystyle{{g}}^{{5}}\usepackage{cmbright}\Huge\$ . Because these variables each have an odd exponent, the expression $\displaystyle{{f}}^{{3}}\usepackage{cmbright}\Huge\$ or $\displaystyle{{g}}^{{5}}\usepackage{cmbright}\Huge\$ could have a positive or negative value. You need to write $\displaystyle\sqrt{{{{\left({{f}}^{{3}}\right)}}^{{2}}}}={\left|{{f}}^{{3}}\right|}\usepackage{cmbright}\Huge\$ and $\displaystyle\sqrt{{{{\left({{g}}^{{5}}\right)}}^{{2}}}}={\left|{{g}}^{{5}}\right|}\usepackage{cmbright}\Huge\$ because the square root symbol means take the positive root.