Chapter 8 - Rational Functions - 8-1 Inverse Variation - Practice and Problem-Solving Exercises - Page 505: 54

$10x^2|y^3|\sqrt{2y}$

Recall: For real numbers $\sqrt[n]{a}$ and $\sqrt[n]{b}$, $$\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$$ Thus, \begin{align*} \sqrt{5x^3} \cdot \sqrt{4xxy^7}&=\sqrt{5x^3 \cdot 40xy^7}\\ &=\sqrt{200x^4y^7}\\ &=\sqrt{100x^4y^6(2y)}\\ &=\sqrt{\left(10x^2y^3\right)^2(2y)}\\ &=10x^2|y^3|\sqrt{2y}\\ \end{align*}