Chapter 8 - Rational Functions - 8-1 Inverse Variation - Practice and Problem-Solving Exercises - Page 505: 53

$84x^2$

Recall: For real numbers $\sqrt[n]{a}$ and $\sqrt[n]{b}$, $$\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$$ Thus, \begin{align*} 3\sqrt[3]{2x^2} \cdot 7\sqrt[3]{32x^4}&=3(7)\sqrt[3]{2x^2 \cdot 32x^4}\\ &=21\sqrt[3]{64x^6}\\ &=21\sqrt[3]{\left(4x^2\right)^3}\\ &=21 \cdot 4x^2\\ &=84x^2 \end{align*}