№6. 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) \(28a^{18}b^{19}:\frac{14a^{20}b^{15}}{15c^4}\).

1. \[\frac{16x^3}{9y^4}:\frac{8x^8}{27y^6}=\frac{16x^3}{9y^4}\cdot\frac{27y^6}{8x^8}=2\cdot3\cdot\frac{y^2}{x^5}=\frac{6y^2}{x^5}.\]
2. \[\frac{18m^3n^4}{25p^6q^{10}}:\left(-\frac{4m^2n^9}{75p^5q^{12}}\right)=\frac{18m^3n^4}{25p^6q^{10}}\cdot\left(-\frac{75p^5q^{12}}{4m^2n^9}\right)=-\frac{27mq^2}{2pn^5}.\]
3. \[28a^{18}b^{19}:\frac{14a^{20}b^{15}}{15c^4}=28a^{18}b^{19}\cdot\frac{15c^4}{14a^{20}b^{15}}=30\frac{c^4b^4}{a^2}=\frac{30b^4c^4}{a^2}.\]

Ответ: 1) \(\frac{6y^2}{x^5}\); 2) \(-\frac{27mq^2}{2pn^5}\); 3) \(\frac{30b^4c^4}{a^2}\).