Simplify each radical and then combine.

$\displaystyle{{x}}^{{2}}{\sqrt[{{4}}]{{{16}{{x}}^{{2}}{{y}}^{{2}}}}}+{x}{\sqrt[{{4}}]{{{81}{{x}}^{{6}}{{y}}^{{2}}}}}={{x}}^{{2}}{\sqrt[{{4}}]{{{16}}}}{\sqrt[{{4}}]{{{{x}}^{{2}}{{y}}^{{2}}}}}+{x}{\sqrt[{{4}}]{{{81}}}}{\sqrt[{{4}}]{{{{x}}^{{4}}}}}{\sqrt[{{4}}]{{{{x}}^{{2}}{{y}}^{{2}}}}}\usepackage{cmbright}\Huge\$

$\displaystyle={2}{{x}}^{{2}}{\sqrt[{{4}}]{{{{x}}^{{2}}{{y}}^{{2}}}}}+{3}{{x}}^{{2}}{\sqrt[{{4}}]{{{{x}}^{{2}}{{y}}^{{2}}}}}={\left({2}{{x}}^{{2}}+{3}{{x}}^{{2}}\right)}{\sqrt[{{4}}]{{{{x}}^{{2}}{{y}}^{{2}}}}}={5}{{x}}^{{2}}{\sqrt[{{4}}]{{{{x}}^{{2}}{{y}}^{{2}}}}}\usepackage{cmbright}\Huge\$