#### Answer

$\sqrt[3] 14xy$

#### Work Step by Step

The product rule for radicals tells us that $\sqrt[n] a\times\sqrt[n] b=\sqrt[n] ab$ (when $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the product of two nth roots is the nth root of the product.
Therefore, $\sqrt[3] 7x\times\sqrt[3] 2y=\sqrt[3] (7x\times 2y)=\sqrt[3] (7\times2\times x\times y)=\sqrt[3] 14xy$.