40.2. Выполните умножение: 1) \(\frac{9}{2a}\cdot\frac{5a}{3}\); 2) \(\frac{5a}{8b}\cdot\frac{7}{10}\); 3) \(\frac{b^2}{10}\cdot\frac{5}{b}\); 4) \(\frac{12x^5}{25}\cdot\frac{15}{8x^2}\); 5) \(\frac{5}{3a}\cdot\frac{2b}{3}\); 6) \(\frac{3x}{4}\cdot\frac{1}{x}\); 7) \(\frac{3b^2}{10}\cdot\frac{15}{b^3}\); 8) \(\frac{16x^5}{35}\cdot\frac{5}{8x^3}\); 9) \(\frac{5a}{8u}\cdot\frac{7}{10}\); 10) \(\frac{9}{2a}\cdot\frac{5a}{3}\); 11) \(\frac{18}{c^4}\cdot\frac{c^3}{24}\); 12) \(\frac{3}{4a^3}\cdot\frac{16a^2}{9}\); 13) \(\frac{15x^3}{4}\cdot\frac{12}{5x}\); 14) \(\frac{15}{3ab}\cdot\frac{12b^3}{3}\); 15) \(\frac{18}{c^4}\cdot\frac{c^3}{24}\).

1. Перемножаем числители и знаменатели, затем сокращаем: \(\frac{9\cdot5a}{2a\cdot3}=\frac{15}{2}\).
2. \(\frac{5a\cdot7}{8b\cdot10}=\frac{7a}{16b}\).
3. \(\frac{b^2\cdot5}{10b}=\frac b2\).
4. \(\frac{12x^5\cdot15}{25\cdot8x^2}=\frac{9x^3}{10}\).
5. \(\frac{5\cdot2b}{3a\cdot3}=\frac{10b}{9a}\).
6. \(\frac{3x}{4x}=\frac34\).
7. \(\frac{3b^2\cdot15}{10b^3}=\frac{9}{2b}\).
8. \(\frac{16x^5\cdot5}{35\cdot8x^3}=\frac{2x^2}{7}\).
9. \(\frac{5a\cdot7}{8u\cdot10}=\frac{7a}{16u}\).
10. \(\frac{9\cdot5a}{2a\cdot3}=\frac{15}{2}\).
11. \(\frac{18c^3}{24c^4}=\frac{3}{4c}\).
12. \(\frac{3\cdot16a^2}{4a^3\cdot9}=\frac{4}{3a}\).
13. \(\frac{15x^3\cdot12}{4\cdot5x}=9x^2\).
14. \(\frac{15\cdot12b^3}{3ab\cdot3}=\frac{20b^2}{a}\).
15. \(\frac{18c^3}{24c^4}=\frac{3}{4c}\).

Ответ: 1) \(\frac{15}{2}\); 2) \(\frac{7a}{16b}\); 3) \(\frac b2\); 4) \(\frac{9x^3}{10}\); 5) \(\frac{10b}{9a}\); 6) \(\frac34\); 7) \(\frac{9}{2b}\); 8) \(\frac{2x^2}{7}\); 9) \(\frac{7a}{16u}\); 10) \(\frac{15}{2}\); 11) \(\frac{3}{4c}\); 12) \(\frac{4}{3a}\); 13) \(9x^2\); 14) \(\frac{20b^2}{a}\); 15) \(\frac{3}{4c}\).