30. Выполните возведение в степень: 1) (m^6/n^3)^2; 2) (-3a/2b^2)^4; 3) (-5a^3b^4/3c^5d^7)^3.

Задание 30: Выполните возведение в степень 1) $(\frac{m^6}{n^3})^2 = \frac{(m^6)^2}{(n^3)^2} = \frac{m^{12}}{n^6}$ 2) $(-\frac{3a}{2b^2})^4 = \frac{(-3a)^4}{(2b^2)^4} = \frac{81a^4}{16b^8}$ 3) $(-\frac{5a^3b^4}{3c^5d^7})^3 = -\frac{125a^9b^{12}}{27c^{15}d^{21}}$ Задание 31: Выполните деление 1) $\frac{16x^3}{9y^4} : \frac{8x^8}{27y^6} = \frac{16x^3}{9y^4} \cdot \frac{27y^6}{8x^8} = \frac{16 \cdot 27 \cdot x^3 \cdot y^6}{9 \cdot 8 \cdot y^4 \cdot x^8} = \frac{2 \cdot 3 \cdot y^2}{x^5} = \frac{6y^2}{x^5}$ 2) $\frac{18m^3n^4}{25p^6q^{10}} : (-\frac{4m^2n^9}{75p^5q^{12}}) = \frac{18m^3n^4}{25p^6q^{10}} \cdot (-\frac{75p^5q^{12}}{4m^2n^9}) = -\frac{18 \cdot 75 \cdot m^3 \cdot n^4 \cdot p^5 \cdot q^{12}}{25 \cdot 4 \cdot p^6 \cdot q^{10} \cdot m^2 \cdot n^9} = -\frac{27 \cdot m \cdot q^2}{2 \cdot p \cdot n^5} = -\frac{27mq^2}{2pn^5}$ 3) $28a^{18}b^{19} : \frac{14a^{20}b^{15}}{15c^4} = 28a^{18}b^{19} \cdot \frac{15c^4}{14a^{20}b^{15}} = \frac{28 \cdot 15 \cdot a^{18} \cdot b^{19} \cdot c^4}{14 \cdot a^{20} \cdot b^{15}} = \frac{2 \cdot 15 \cdot b^4 \cdot c^4}{a^2} = \frac{30b^4c^4}{a^2}$ 4) $\frac{48x^4y^3}{49z^9} : (16x^7y^8) = \frac{48x^4y^3}{49z^9} \cdot \frac{1}{16x^7y^8} = \frac{48 \cdot x^4 \cdot y^3}{49 \cdot 16 \cdot z^9 \cdot x^7 \cdot y^8} = \frac{3}{49x^3y^5z^9}$ 5) $\frac{11a^5b^{12}}{12cd^6} : \frac{55a^3b^2}{18c^7d^4} : \frac{21b^6d^2}{20a^7c^3} = \frac{11a^5b^{12}}{12cd^6} \cdot \frac{18c^7d^4}{55a^3b^2} \cdot \frac{20a^7c^3}{21b^6d^2} = \frac{11 \cdot 18 \cdot 20 \cdot a^5 \cdot a^7 \cdot b^{12} \cdot c^7 \cdot c^3 \cdot d^4}{12 \cdot 55 \cdot 21 \cdot c \cdot c^3 \cdot d^6 \cdot d^2 \cdot a^3 \cdot b^2 \cdot b^6} = \frac{3960 a^{12} b^{12} c^{10} d^4}{13860 a^3 b^8 c^4 d^8} = \frac{2a^9b^4c^6}{7d^4}$ 6) $(-\frac{2p^4q^2}{5m^8})^3 : (-\frac{2p^5q^3}{5m^6})^4 = (-\frac{8p^{12}q^6}{125m^{24}}) : \frac{16p^{20}q^{12}}{625m^{24}} = -\frac{8p^{12}q^6}{125m^{24}} \cdot \frac{625m^{24}}{16p^{20}q^{12}} = -\frac{8 \cdot 625 \cdot p^{12} \cdot q^6 \cdot m^{24}}{125 \cdot 16 \cdot m^{24} \cdot p^{20} \cdot q^{12}} = -\frac{5}{2p^8q^6}$