Упражнение 156

\(1)\ \frac{3a^4b^3}{10c^5}\cdot\frac{4b^4c^2}{27a^7}:\frac{5b^7}{9a^3c^3}=\frac{3a^4b^3}{10c^5}\cdot\frac{4b^4c^2}{27a^7}\cdot\frac{9a^3c^3}{5b^7}=\frac{3a^4b^3\cdot4b^4c^2\cdot9a^3c^3}{10c^5\cdot27a^7\cdot5b^7}=\frac{3\cdot4\cdot9\cdot{a}^7b^7c^5}{10\cdot27\cdot5\cdot{a}^7b^7c^5}=\frac{2}{25};\)

\(2)\ \frac{3a^2}{2b^2c^2}:\frac{7c^8}{6b^3}:\frac{9ab}{14c^{12}}=\frac{3a^2}{2b^2c^2}\cdot\frac{6b^3}{7c^8}\cdot\frac{14c^{12}}{9ab}=\frac{3a^2\cdot6b^3\cdot14c^{12}}{2b^2c^2\cdot7c^8\cdot9ab}=\frac{3\cdot6\cdot14\cdot{a}^2b^3c^{12}}{2\cdot7\cdot9\cdot{a}b^3c^{10}}=2ac^2;\)

\(3)\ \left(\frac{5a^3}{b^4}\right)^4\cdot\frac{b^{18}}{50a^{16}}=\frac{ (5a^3)^4}{ (b^4)^4}\cdot\frac{b^{18}}{50a^{16}}=\frac{5^4a^{12}}{b^{16}}\cdot\frac{b^{18}}{2\cdot5^2a^{16}}=\frac{5^4a^{12}\cdot{b}^{18}}{b^{16}\cdot2\cdot5^2a^{16}}=\frac{25b^2}{2a^4};\)

\(4)\ \left(\frac{3x^7}{y^{10}}\right)^4:\left(\frac{3x^6}{y^8}\right)^3=\left(\frac{3x^7}{y^{10}}\right)^4\cdot\left(\frac{y^8}{3x^6}\right)^3=\frac{ (3x^7)^4}{ (y^{10})^4}\cdot\frac{ (y^8)^3}{ (3x^6)^3}=\frac{3^4x^{28}}{y^{40}}\cdot\frac{y^{24}}{3^3x^{18}}=\frac{3^4x^{28}\cdot{y}^{24}}{y^{40}\cdot3^3x^{18}}=\frac{3x^{10}}{y^{16}}.\)