Answer
$300\sqrt[3]{3}$
Work Step by Step
Use the rule $\sqrt[n]{a^m}=a^{\frac{m}{n}}$ to obtain:
$(\sqrt[3]{3}\sqrt{10})^4=\left(3^{\frac{1}{3}}10^{\frac{1}{2}}\right)^4$
Use the rule $\left(a^m\right)^n=a^{mn}$ to obtain:
$=3^{\frac{1}{3}\cdot 4}10^{\frac{1}{2}\cdot 4}$
$=3^{\frac{4}{3}}10^{2}$
Simplify.
$=3^{\frac{3+1}{3}}\cdot100$
$=3^{1+\frac{1}{3}}\cdot100$
$=3\cdot 3^{\frac{1}{3}}\cdot100$
$=300\cdot 3^{\frac{1}{3}}$
$=300 \sqrt[3]{3}$
Hence, the correct answer is $300\sqrt[3]{3}$.
