Выполните деление: 1) $\frac{16x^3}{9y^4} : \frac{8x^8}{27y^6}; 2) \frac{18m^3n^4}{25p^6q^{10}} : \left(-\frac{4m^2n^9}{75p^5q^{12}}\right); 3) 28a^{18}b^{19} : \frac{14a^{20}b^{15}}{15c^4}$

Question

Вопрос: $Фото задания: Выполните деление: 1) \(\frac{16x^3}{9y^4} : \frac{8x^8}{27y^6}; 2) \frac{18m^3n^4}{25p^6q^{10}} :…$ Фото задания

Accepted Answer

$\frac{16x^3}{9y^4} : \frac{8x^8}{27y^6} = \frac{16x^3}{9y^4} \cdot \frac{27y^6}{8x^8} = \frac{16 ∙ 27 ∙ x^3 ∙ y^6}{9 ∙ 8 ∙ x^8 ∙ y^4} = \frac{2 ∙ 3 ∙ y^2}{x^5} = \frac{6y^2}{x^5}$
$\frac{18m^3n^4}{25p^6q^{10}} : \left(-\frac{4m^2n^9}{75p^5q^{12}}\right) = \frac{18m^3n^4}{25p^6q^{10}} \cdot \left(-\frac{75p^5q^{12}}{4m^2n^9}\right) = -\frac{18 ∙ 75 ∙ m^3 ∙ n^4 ∙ p^5 ∙ q^{12}}{25 ∙ 4 ∙ m^2 ∙ n^9 ∙ p^6 ∙ q^{10}} = -\frac{18 ∙ 3 ∙ m ∙ q^2}{p ∙ 4 ∙ n^5} = -\frac{54mq^2}{4pn^5} = -\frac{27mq^2}{2pn^5}$
$28a^{18}b^{19} : \frac{14a^{20}b^{15}}{15c^4} = 28a^{18}b^{19} \cdot \frac{15c^4}{14a^{20}b^{15}} = \frac{28 ∙ 15 ∙ a^{18} ∙ b^{19} ∙ c^4}{14 ∙ a^{20} ∙ b^{15}} = \frac{2 ∙ 15 ∙ b^4 ∙ c^4}{a^2} = \frac{30b^4c^4}{a^2}$

Выполните деление: 1) \(\frac{16x^3}{9y^4} : \frac{8x^8}{27y^6}; 2) \frac{18m^3n^4}{25p^6q^{10}} : \left(-\frac{4m^2n^9}{75p^5q^{12}}\right); 3) 28a^{18}b^{19} : \frac{14a^{20}b^{15}}{15c^4}\)