You may have multiplied correctly, but then you found the square root of the radical instead of the 4th root. The correct value of the original expression is $\displaystyle{\sqrt[{{4}}]{{{81}{{x}}^{{12}}{{y}}^{{8}}}}}\usepackage{cmbright}\Huge\$ . Identify powers of 4, rewrite the expression as a product, and simplify by using: $\displaystyle{\sqrt[{{4}}]{{{{a}}^{{4}}}}}={a}\usepackage{cmbright}\Huge\$