## Functions Modeling Change: A Preparation for Calculus, 5th Edition

$9x^5$
Use the fact that $\sqrt{a} \equiv a^\frac{1}{2}$, $$(3x(x^3)^\frac{1}{2})^2$$ Since $(a^m)^n=a^{mn}$, the expression becomes $$(3x(x^\frac{3}{2})^2$$ Finally, since $(ab)^n=a^nb^n$ and $a^m(a^n)=a^{m+n}$, the expression simplifies to $$3^2 \cdot x^2 \cdot x^{(3/2)(2)}=9x^2 \cdot x^3=9x^5$$