Упростите выражение:
1) $\frac{3a^4b^3}{10c^5} * \frac{4b^4c^2}{27a^7} : \frac{5b^7}{9a^3c^3}$;
2) $\frac{3a^2}{2b^2c^2} : \frac{7c^8}{6b^3} : \frac{9ab}{14c^{12}}$;
3) $(\frac{5a^3}{b^4})^4 * \frac{b^{18}}{50a^{16}}$;
4) $(\frac{3x^7}{y^{10}})^4 : (\frac{3x^6}{y^8})^3$.
$\frac{3a^4b^3}{10c^5} * \frac{4b^4c^2}{27a^7} : \frac{5b^7}{9a^3c^3} = \frac{3a^4b^3}{10c^5} * \frac{4b^4c^2}{27a^7} * \frac{9a^3c^3}{5b^7} = \frac{1}{5} * \frac{2}{1} * \frac{1}{5} = \frac{2}{25}$
$\frac{3a^2}{2b^2c^2} : \frac{7c^8}{6b^3} : \frac{9ab}{14c^{12}} = \frac{3a^2}{2b^2c^2} * \frac{6b^3}{7c^8} * \frac{14c^{12}}{9ab} = \frac{a}{1} * \frac{1}{1} * \frac{2c^{2}}{1} = 2ac^2$
$(\frac{5a^3}{b^4})^4 * \frac{b^{18}}{50a^{16}} = \frac{5^4a^{12}}{b^{16}} * \frac{b^{18}}{2 * 5^2a^{16}} = \frac{5^2}{1} * \frac{b^{2}}{2a^{4}} = \frac{25b^2}{2a^4}$
$(\frac{3x^7}{y^{10}})^4 : (\frac{3x^6}{y^8})^3 = \frac{3^4x^{28}}{y^{40}} : \frac{3^3x^{18}}{y^{24}} = \frac{3^4x^{28}}{y^{40}} * \frac{y^{24}}{3^3x^{18}} = \frac{3x^{10}}{y^{16}} * \frac{1}{1} = \frac{3x^{10}}{y^{16}}$
Пожауйста, оцените решение
