Answer
$15 \sqrt[3]{3}$
Work Step by Step
Use $9=3^2$ to obtain:
$(\sqrt{5}\sqrt[3]{9})^2=(\sqrt{5}\sqrt[3]{3^2})^2$
Use the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$ to obtain:
$=\left(5^{\frac{1}{2}}3^{\frac{2}{3}}\right)^2$
Use the Power Rule $\left(a^m\right)^n=a^{mn}$ to obtain:
$=5^{\frac{1}{2}\cdot 2}3^{\frac{2}{3}\cdot 2}$
$=5^{1}3^{\frac{4}{3}}$
Simplify.
$=5\cdot3^{\frac{3+1}{3}}$
$=5\cdot3^{1+\frac{1}{3}}$
$=5\cdot3\cdot 3^{\frac{1}{3}}$
$=15\cdot 3^{\frac{1}{3}}$
$=15\cdot \sqrt[3]{3}$
Hence, the correct answer is $15 \sqrt[3]{3}$.
