Answer
Answer choice $A$: $4a^{\frac{2}{3}}b^\frac{1}{3}$
Work Step by Step
The expression is the same thing as
$(64a^2b)^{\frac{1}{3}}$
Use the distributive property
$4 \times a ^{\frac{2}{3}} \times b^{\frac{1}{3}}$
$\boxed{4a^{\frac{2}{3}}{b^\frac{1}{3}}}$