Выполните деление: 1) \(\frac{6x^2y}{5z}:\frac{3xy^2}{10z^2}\); 2) \(\frac{15a^3b^2}{7c}:\frac{25a^2b}{14c^3}\); 3) \(\frac{8m^4n}{9k}:\frac{12m^2n^3}{15k^2}\); 4) \(\frac{24p^5q^3}{11r}:\frac{16p^3q}{33r^4}\); 5) \(\frac{30u^6v^2}{13w}:\frac{45u^4v^5}{26w^3}\); 6) \(\left(-\frac{6m^4n^2}{p^2}\right):\left(-\frac{3m^2n}{p^3}\right)\).

Заменяем деление умножением на обратную дробь и сокращаем общие множители.

1. \(\frac{6x^2y}{5z}\cdot\frac{10z^2}{3xy^2}=\frac{4xz}{y}\).
2. \(\frac{15a^3b^2}{7c}\cdot\frac{14c^3}{25a^2b}=\frac{6abc^2}{5}\).
3. \(\frac{8m^4n}{9k}\cdot\frac{15k^2}{12m^2n^3}=\frac{10m^2k}{9n^2}\).
4. \(\frac{24p^5q^3}{11r}\cdot\frac{33r^4}{16p^3q}=\frac{9p^2q^2r^3}{2}\).
5. \(\frac{30u^6v^2}{13w}\cdot\frac{26w^3}{45u^4v^5}=\frac{4u^2w^2}{3v^3}\).
6. \(-\frac{6m^4n^2}{p^2}\cdot\left(-\frac{p^3}{3m^2n}\right)=2m^2np\).

Ответ: 1) \(\frac{4xz}{y}\); 2) \(\frac{6abc^2}{5}\); 3) \(\frac{10m^2k}{9n^2}\); 4) \(\frac{9p^2q^2r^3}{2}\); 5) \(\frac{4u^2w^2}{3v^3}\); 6) \(2m^2np\).