Answer
$\color{blue}{(4xy+5x^2)\sqrt[4]{xy^2}}$
Work Step by Step
Simplify each radical.
Factor the radicand so that one factor is a perfect fourth power, then bring out the fourth root of the perfect fourth power factor to obtain:
$=\sqrt[4]{256x^4y^4(xy^2)}+\sqrt[4]{625x^8(xy^2)}
\\=\sqrt[4]{4^4x^4y^4(xy^2)} + \sqrt[4]{5^4(x^2)^4(xy^2)}
\\=4xy\sqrt[4]{xy^2}+5x^2\sqrt[4]{xy^2}$
Combine like terms to obtain:
$\\=\color{blue}{(4xy+5x^2)\sqrt[4]{xy^2}}$
