Answer
$x^{4}\sqrt[3] (50x^{2})$
Work Step by Step
$\sqrt [3] (50x^{14})=\sqrt [3] (x^{12}\times50x^{2})=\sqrt [3] (x^{12})\times \sqrt[3] (50x^{2})=x^{4}\sqrt[3] (50x^{2})$
We know that $\sqrt[3] (x^{12})=x^{4}$, because $(x^{4})^{3}=x^{4\times3}=x^{12}$.