Answer
$a^\frac{2}{3}$
Work Step by Step
Recall the rational exponent property (pg. 382):
$a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$
Applying this property, we get:
$\sqrt[3]{a^2}=(a^2)^{1/3}$
Next, recall the basic exponent property (pg. 360):
$(a^m)^n=a^{mn}$
Applying this property, we get:
$\left(a^2\right)^{\frac{1}{3}}=a^\frac{2}{3}$
