3. Выполните действия 1) (8m)/n : (4m)/n 2) - (9a)/b^5 * (b^3)/(18a^4) 3) (a^2-25)/(a+7) * (a+7)/(a-5) 4) (x-y)/(xy) : (x^2-y^2)/(3xy) 5) (c-5)/(c^2-4c) : (c-5)/(5c-20) 6) ((5a^6)/b^5)^2 7) ((-4m)/(9n^3))^2

1) $$ \frac{8m}{n} : \frac{4m}{n} = \frac{8m}{n} \cdot \frac{n}{4m} = \frac{8mn}{4mn} = 2 $$.

2) $$ - \frac{9a}{b^5} \cdot \frac{b^3}{18a^4} = - \frac{9ab^3}{18a^4b^5} = - \frac{1}{2a^3b^2} $$.

3) $$ \frac{a^2-25}{a+7} \cdot \frac{a+7}{a-5} = \frac{(a-5)(a+5)}{a+7} \cdot \frac{a+7}{a-5} = a+5 $$.

4) $$ \frac{x-y}{xy} : \frac{x^2-y^2}{3xy} = \frac{x-y}{xy} \cdot \frac{3xy}{x^2-y^2} = \frac{x-y}{xy} \cdot \frac{3xy}{(x-y)(x+y)} = \frac{3}{x+y} $$.

5) $$ \frac{c-5}{c^2-4c} : \frac{c-5}{5c-20} = \frac{c-5}{c(c-4)} \cdot \frac{5(c-4)}{c-5} = \frac{5}{c} $$.

6) $$ (\frac{5a^6}{b^5})^2 = \frac{25a^{12}}{b^{10}} $$.

7) $$ (\frac{-4m}{9n^3})^2 = \frac{16m^2}{81n^6} $$.

Ответ: 1) $$2$$; 2) $$\frac{-1}{2a^3b^2}$$; 3) $$a+5$$; 4) $$\frac{3}{x+y}$$; 5) $$\frac{5}{c}$$; 6) $$\frac{25a^{12}}{b^{10}}$$; 7) $$\frac{16m^2}{81n^6}$$