Answer
$\dfrac{16}{81}$
Work Step by Step
Recall, the exponent tells us how many times to multiply the base (which is the fraction in this case) by itself. Thus, we obtain:
$\left(\dfrac{2}{3}\right)^4=\left(\dfrac{2}{3}\right)\left(\dfrac{2}{3}\right)\left(\dfrac{2}{3}\right)\left(\dfrac{2}{3}\right)=\dfrac{16}{81}$