You may have thought that the 4th root of 9 meant $\displaystyle{9}\div{4}\usepackage{cmbright}\Huge\$ , which results in 2.25. To simplify the expression in the problem, multiply the factors under one radical sign:

$\displaystyle{\sqrt[{{4}}]{{{9}{{x}}^{{5}}{{y}}^{{2}}}}}\cdot{\sqrt[{{4}}]{{{9}{{x}}^{{5}}{{y}}^{{4}}}}}\cdot{\sqrt[{{4}}]{{{{x}}^{{2}}{{y}}^{{2}}}}}={\sqrt[{{4}}]{{{9}{{x}}^{{5}}{{y}}^{{2}}\cdot{9}{{x}}^{{5}}{{y}}^{{4}}\cdot{{x}}^{{2}}{{y}}^{{2}}}}}\usepackage{cmbright}\Huge\$

Apply the laws of exponents. Identify powers of 4, rewrite the expression as a product, and simplify by using: $\displaystyle{\sqrt[{{4}}]{{{{a}}^{{4}}}}}={a}\usepackage{cmbright}\Huge\$