Simplify each radical and combine like terms.

$\displaystyle{\sqrt[{{4}}]{{{81}{{x}}^{{6}}{{y}}^{{4}}}}}-{y}{\sqrt[{{4}}]{{{{x}}^{{6}}}}}={\sqrt[{{4}}]{{{{3}}^{{4}}\cdot{{x}}^{{4}}\cdot{{x}}^{{2}}\cdot{{y}}^{{4}}}}}-{y}{\sqrt[{{4}}]{{{{x}}^{{4}}\cdot{{x}}^{{2}}}}}\usepackage{cmbright}\Huge\$

$\displaystyle={3}{x}{y}{\sqrt[{{4}}]{{{{x}}^{{2}}}}}-{x}{y}{\sqrt[{{4}}]{{{{x}}^{{2}}}}}\usepackage{cmbright}\Huge\$

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