#### Answer

$-\frac{6a^{2}}{5}$

#### Work Step by Step

We can never divide fractions. Rather, we must flip the numerator and the denominator for the second fraction listed and then multiply.
$\frac{24ab^{2}}{25b}\div\frac{-12ab}{15a^{2}}=\frac{24ab^{2}}{25b}\times\frac{15a^{2}}{-12ab}$
When we multiply fractions, we multiply the numerators of the fractions by each other and the denominators of the fractions by each other. Then, we cancel out the common factors in the numerator and the denominator of the resultant fraction in order to simplify the fraction:
$\frac{24ab^{2}}{25b}\times\frac{15a^{2}}{-12ab}$
=$\frac{24ab^{2} \times 15a^{2}}{25b \times -12ab}$
=$\frac{360a^{1+2}b^{2}}{-300ab^{1+1}}$
=$\frac{360a^{3}b^{2}}{-300ab^{2}}$
=$\frac{36a^{3-1}b^{2-2}}{-30}$
=$\frac{36a^{2}b^{0}}{-30}$
=$\frac{6a^{2}(1)}{-5}$
=$-\frac{6a^{2}}{5}$