Answer
$5xy^4 \sqrt[3] {x^2y^2}$
Work Step by Step
Apply product rule: $\sqrt[n] p \sqrt[n] q=\sqrt[n]{pq}$
Here, $n$ refers as index.
$\sqrt[3] {25x^4y^2} \sqrt[3] {5xy^{12}}=\sqrt {(25x^4y^2) (5xy^{12})}= \sqrt[3]{125x^5y^{14}}$
The radical $\sqrt[3]{125x^5y^{14}}$ can be further simplified by using product rule again.
Such as:
$\sqrt[3]{125x^5y^{14}}=\sqrt[3] {(5xy^4)^3 (x^2y^2)}=\sqrt[3] {(5xy^4)^3} \sqrt[3]{ (x^2y^2)}=5xy^4 \sqrt[3] {x^2y^2}$
