Answer
$\frac{3y^{14}}{4x^{4}}$
Work Step by Step
$$\frac{24x^{3}y^{5}}{32x^{7}y^{-9}}$$
Group factors with like bases:
$$=(\frac{24}{32}))(\frac{x^{3}}{x^{7}})(\frac{y^{5}}{y^{-9}})$$
$$=\frac{3}{4}x^{(3-7)}y^{(5-(-9))}$$
$$=\frac{3}{4}x^{-4}y^{(5+9)}$$
$$=\frac{3}{4}x^{-4}y^{14}$$
Write as a fraction, move the base with the negative exponent to the other side of the fraction, and make the exponent positive:
$$=\frac{3y^{14}}{4x^{4}}$$
