№ 433. Выполните действие: а) \(\frac{3}{4}\cdot\frac{5}{7}\); б) \(\frac{1}{8}\cdot\frac{3}{4}\); в) \(\frac{4}{7}\cdot\frac{5}{6}\); г) \(\frac{2}{5}\cdot\frac{7}{11}\); д) \(\frac{1}{2}\cdot\frac{4}{9}\); е) \(\frac{11}{12}\cdot\frac{8}{9}\); ж) \(\frac{2}{5}\cdot\frac{3}{2}\); з) \(\frac{11}{15}\cdot\frac{3}{5}\); и) \(\frac{15}{16}\cdot\frac{5}{9}\); к) \(\frac{12}{25}\cdot\frac{9}{16}\); л) \(\frac{14}{17}\cdot\frac{34}{63}\); м) \(\frac{17}{26}\cdot\frac{13}{18}\); н) \(\left(\frac{4}{5}\right)^2\); о) \(\left(\frac{2}{3}\right)^3\); п) \(\left(\frac{1}{7}\right)^2\).

Перемножаем числители и знаменатели, предварительно сокращая дроби:

1. а) \(\frac{3}{4}\cdot\frac{5}{7}=\frac{15}{28}\);
2. б) \(\frac{1}{8}\cdot\frac{3}{4}=\frac{3}{32}\);
3. в) \(\frac{4}{7}\cdot\frac{5}{6}=\frac{10}{21}\);
4. г) \(\frac{2}{5}\cdot\frac{7}{11}=\frac{14}{55}\);
5. д) \(\frac{1}{2}\cdot\frac{4}{9}=\frac{2}{9}\);
6. е) \(\frac{11}{12}\cdot\frac{8}{9}=\frac{22}{27}\);
7. ж) \(\frac{2}{5}\cdot\frac{3}{2}=\frac{3}{5}\);
8. з) \(\frac{11}{15}\cdot\frac{3}{5}=\frac{11}{25}\);
9. и) \(\frac{15}{16}\cdot\frac{5}{9}=\frac{25}{48}\);
10. к) \(\frac{12}{25}\cdot\frac{9}{16}=\frac{27}{100}\);
11. л) \(\frac{14}{17}\cdot\frac{34}{63}=\frac{4}{27}\);
12. м) \(\frac{17}{26}\cdot\frac{13}{18}=\frac{17}{36}\);
13. н) \(\left(\frac{4}{5}\right)^2=\frac{16}{25}\);
14. о) \(\left(\frac{2}{3}\right)^3=\frac{8}{27}\);
15. п) \(\left(\frac{1}{7}\right)^2=\frac{1}{49}\).

Ответ: а) \(\frac{15}{28}\); б) \(\frac{3}{32}\); в) \(\frac{10}{21}\); г) \(\frac{14}{55}\); д) \(\frac{2}{9}\); е) \(\frac{22}{27}\); ж) \(\frac{3}{5}\); з) \(\frac{11}{25}\); и) \(\frac{25}{48}\); к) \(\frac{27}{100}\); л) \(\frac{4}{27}\); м) \(\frac{17}{36}\); н) \(\frac{16}{25}\); о) \(\frac{8}{27}\); п) \(\frac{1}{49}\).