Chapter 8 - Rational Functions - 8-1 Inverse Variation - Practice and Problem-Solving Exercises - Page 505: 52

$-90x^2$

Recall: For real numbers $\sqrt[n]{a}$ and $\sqrt[n]{b}$, $$\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$$ Thus, \begin{align*} -5\sqrt{6x} \cdot 3\sqrt{6x^3}&=-5(3)\sqrt{6x \cdot 6x^3}\\ &=-15\sqrt{6^2x^4}\\ &=-15\sqrt{\left(6x^2\right)^2}\\ &=-15 \cdot 6x^2\\ &=-90x^2 \end{align*}