13. Выполните умножение:

1. a) $$-\frac{10x^2y^2}{9a^2} \cdot \frac{27a^3}{5xy} = -\frac{10 \cdot 27 x^2 y^2 a^3}{9 \cdot 5 a^2 x y} = -\frac{2 \cdot 3 x y a}{1} = -6axy$$
2. б) $$\frac{2m^3}{35a^3b^2} \cdot (-\frac{7a^2b}{6m}) = -\frac{2 \cdot 7 m^3 a^2 b}{35 \cdot 6 a^3 b^2 m} = -\frac{1 \cdot 1 m^2}{5 \cdot 3 a b} = -\frac{m^2}{15ab}$$
3. в) $$\frac{13x}{12mn^2} \cdot 4m^2n = \frac{13 \cdot 4 x m^2 n}{12 m n^2} = \frac{13 x m}{3 n}$$
4. г) $$-ab \cdot (-\frac{11x^2}{3a^2b^2}) = \frac{11abx^2}{3a^2b^2} = \frac{11x^2}{3ab}$$

Упростите выражение:

1. ) $$\frac{2a^2b}{3xy} \cdot \frac{3x^2y}{4ab^2} \cdot \frac{6ax}{15b^2} = \frac{2 \cdot 3 \cdot 6 a^3 b x^2 y}{3 \cdot 4 \cdot 15 x^2 y b^4 a} = \frac{36 a^3 b x^2 y}{180 a x^2 y b^4} = \frac{1 a^2}{5 b^3} = \frac{a^2}{5b^3}$$
2. б) $$\frac{6m^3n^2}{35p^3} \cdot \frac{49n^4}{m^5p^3} \cdot \frac{5m^4p^2}{42n^6} = \frac{6 \cdot 49 \cdot 5 m^7 n^6 p^2}{35 \cdot 42 m^5 p^6 n^6} = \frac{1 \cdot 7 \cdot 1 m^2}{1 \cdot 6 p^4 1} = \frac{7m^2}{6p^4}$$

зведите в степень:

1. ) $$(\frac{x}{2y})^3 = \frac{x^3}{(2y)^3} = \frac{x^3}{8y^3}$$
2. б) $$(\frac{3a}{c})^4 = \frac{(3a)^4}{c^4} = \frac{81a^4}{c^4}$$
3. в) $$(\frac{n^2}{10m})^3 = \frac{(n^2)^3}{(10m)^3} = \frac{n^6}{1000m^3}$$