Решение:

a) $$\frac{24a^4}{b^3} \cdot \frac{b^4}{8a^2} = \frac{24a^4b^4}{8a^2b^3} = \frac{3a^2b}{1} = 3a^2b$$

б) $$\frac{7xy^2}{2} : 14x^2y^2 = \frac{7xy^2}{2} \cdot \frac{1}{14x^2y^2} = \frac{7xy^2}{28x^2y^2} = \frac{1}{4x}$$

в) $$\frac{m+2n}{m-n} : \frac{m^2-n^2}{5m+10n} = \frac{m+2n}{m-n} \cdot \frac{5m+10n}{m^2-n^2} = \frac{(m+2n) \cdot 5(m+2n)}{(m-n)(m-n)(m+n)} = \frac{5(m+2n)^2}{(m-n)(m+n)} $$

г) $$\frac{x^2-2x+1}{x^2-25} : \frac{x-1}{x^2+5x} = \frac{(x-1)^2}{(x-5)(x+5)} \cdot \frac{x(x+5)}{x-1} = \frac{(x-1)(x-1) \cdot x(x+5)}{(x-5)(x+5)(x-1)} = \frac{x(x-1)}{x-5}$$

Ответ:

1. $$3a^2b$$
2. $$\frac{1}{4x}$$
3. $$\frac{5(m+2n)^2}{(m-n)(m+n)} $$
4. $$\frac{x(x-1)}{x-5}$$