#### Answer

$$\frac{4xy^5}{9}$$

#### Work Step by Step

We know the following rules of exponents. The list of names is on page 330.
$$ (1) \ a^m\cdot a^n = a^{m+n} \\ (2) \ (ab)^m =a^mb^m \\ (3) \ (a^m)^n =a^{mn} \\ (4)
\ a^{-m} = \frac{1}{a^m} \\ (5)\ \frac{a^m}{a^n} =a^{m-n} \\ (6) \ a^0=1 \\ (7) \ (\frac{a}{b})^m =\frac{a^m}{b^m}$$
Thus, we find:
$$ \frac{32x^{-3}y^4\cdot \:3x}{24x^{-3}y^{-2}\cdot \:9y} \\ \frac{96xy^4}{216y^{-1}}\\ \frac{4xy^5}{9}$$