#### Answer

$\sqrt[4] 6x^{3}

#### 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, $\sqrt[4] 2x\times\sqrt[4] 3x^{2}=\sqrt[4] (2x\times 3x^{2})=\sqrt[4] (2\times3\times x\times x^{2})=\sqrt[4] 6x^{3}$.