Упрости выражение, выполни возведение в степень, выполни деление.

29. Упрости выражение: 1) $\frac{ab-b^2}{8} \cdot \frac{32a}{b^3} = \frac{b(a-b)}{8} \cdot \frac{32a}{b^3} = \frac{4a(a-b)}{b^2} = \frac{4a^2 - 4ab}{b^2}$ 2) $\frac{m^2 - mn}{m^2 + mn} \cdot \frac{m^2n + mn^2}{m^3 - m^2n} = \frac{m(m-n)}{m(m+n)} \cdot \frac{mn(m+n)}{m^2(m-n)} = \frac{n}{m}$ 3) $\frac{x^2-16}{x^3-3x^2} \cdot \frac{x^2}{x^2+4x} = \frac{(x-4)(x+4)}{x^2(x-3)} \cdot \frac{x^2}{x(x+4)} = \frac{x-4}{x-3}$ 4) $\frac{5y^2 - 20y + 20}{y^3 - 1} \cdot \frac{3y^2 + 3y + 3}{10y - 20} = \frac{5(y^2 - 4y + 4)}{(y-1)(y^2+y+1)} \cdot \frac{3(y^2 + y + 1)}{10(y-2)} = \frac{5(y-2)^2}{(y-1)(y^2+y+1)} \cdot \frac{3(y^2 + y + 1)}{10(y-2)} = \frac{3(y-2)}{2(y-1)}$ 30. Выполни возведение в степень: 1) $(\frac{m^6}{n^3})^2 = \frac{m^{12}}{n^6}$ 2) $(-\frac{3a}{2b^2})^4 = \frac{81a^4}{16b^8}$ 3) $(\frac{5a^3b^4}{3c^5d^7})^3 = \frac{125a^9b^{12}}{27c^{15}d^{21}}$ 31. Выполни деление: 1) $\frac{16x^3}{9y^4} : \frac{8x^{-8}}{27y^6} = \frac{16x^3}{9y^4} \cdot \frac{27y^6}{8x^{-8}} = \frac{2x^3}{y^4} \cdot \frac{3y^6}{x^{-8}} = 6x^{11}y^2$ 2) $\frac{18m^3n^4}{25p^6q^{10}} : (-\frac{4m^2n^9}{75p^5q^{12}}) = \frac{18m^3n^4}{25p^6q^{10}} \cdot (-\frac{75p^5q^{12}}{4m^2n^9}) = -\frac{27mq^2}{2pn^5}$ 3) $28a^{18}b^{19} : \frac{14a^{20}b^{15}}{15c^4} = 28a^{18}b^{19} \cdot \frac{15c^4}{14a^{20}b^{15}} = \frac{30b^4c^4}{a^2}$ 4) $\frac{48x^4y^3}{49z^9} : (16x^7y^8) = \frac{48x^4y^3}{49z^9} \cdot \frac{1}{16x^7y^8} = \frac{3}{49x^3y^5z^9}$ 5) $\frac{11a^5b^{12}}{12cd^6} : \frac{55a^3b^2}{18c^7d^4} : \frac{21b^6d^2}{20a^7c^3} = \frac{11a^5b^{12}}{12cd^6} \cdot \frac{18c^7d^4}{55a^3b^2} \cdot \frac{20a^7c^3}{21b^6d^2} = \frac{3a^9b^4c^4d^{-4}}{7}$ 6) $(\frac{2p^4q^2}{5m^8})^3 : (\frac{2p^3q^3}{5m^6})^4 = \frac{8p^{12}q^6}{125m^{24}} : \frac{16p^{12}q^{12}}{625m^{24}} = \frac{8p^{12}q^6}{125m^{24}} \cdot \frac{625m^{24}}{16p^{12}q^{12}} = \frac{5}{2q^6}$ 32. Выполни деление: 1) $\frac{x+1}{3x} : \frac{x^2+2x+1}{9x^2} = \frac{x+1}{3x} \cdot \frac{9x^2}{(x+1)^2} = \frac{3x}{x+1}$ 2) $\frac{x^2-2x}{3x+3} : \frac{5x-10}{x+1} = \frac{x(x-2)}{3(x+1)} \cdot \frac{x+1}{5(x-2)} = \frac{x}{15}$ 3) $\frac{n-7}{1} : \frac{n^2-14n+49}{n^2-49} = \frac{n-7}{1} \cdot \frac{(n-7)(n+7)}{(n-7)^2} = n+7$ 4) $\frac{a^2-4b^2}{9a^2-b^2} : \frac{a^2+4ab+4b^2}{9a^2-6ab+b^2} = \frac{(a-2b)(a+2b)}{(3a-b)(3a+b)} : \frac{(a+2b)^2}{(3a-b)^2} = \frac{(a-2b)(a+2b)}{(3a-b)(3a+b)} \cdot \frac{(3a-b)^2}{(a+2b)^2} = \frac{(a-2b)(3a-b)}{(3a+b)(a+2b)}$