#### Answer

$\frac{16}{27}$

#### Work Step by Step

Exponents represent repeated multiplication.
Eliminate common factors to simplify the multiplication.
$9(\frac{1}{3})^{3}(\frac{4}{3})^{2}$ = $(\frac{/\!\!3\times/\!\!3}{1})(\frac{1}{/\!\!3})(\frac{1}{/\!\!3})(\frac{1}{3})(\frac{4}{3})(\frac{4}{3})$ = $(\frac{1}{1})(\frac{1}{1})(\frac{1}{1})(\frac{1}{3})(\frac{4}{3})(\frac{4}{3})$ = $\frac{16}{27}$