You may have incorrectly thought 1 was the 4th root of 4. To simplify this expression, multiply the factors under one radical sign:

$\displaystyle{\sqrt[{{4}}]{{{4}{{x}}^{{2}}{{y}}^{{5}}}}}\cdot{\sqrt[{{4}}]{{{4}{{x}}^{{3}}{{y}}^{{5}}}}}\cdot{\sqrt[{{4}}]{{{{x}}^{{7}}{{y}}^{{2}}}}}={\sqrt[{{4}}]{{{4}{{x}}^{{2}}{{y}}^{{5}}\cdot{4}{{x}}^{{3}}{{y}}^{{5}}\cdot{{x}}^{{7}}{{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\$ .