Answer
$\frac{8}{27}$
Work Step by Step
An exponent of $3$ over the whole fraction means that we raise both the numerator and the denominator to the power of $3$:
$(\frac{2}{3})^{3}=\frac{2^{3}}{3^{3}}=\frac{2\times2\times2}{3\times3\times3}=\frac{8}{27}$