3.60 Выполните действия:

Решение:

а) \( \left(2\frac{1}{2}\right)^2 \cdot \frac{8}{15} - \frac{5}{9} = \left(\frac{5}{2}\right)^2 \cdot \frac{8}{15} - \frac{5}{9} = \frac{25}{4} \cdot \frac{8}{15} - \frac{5}{9} = \frac{5 \cdot 1}{1 \cdot 1} \cdot \frac{2}{3} - \frac{5}{9} = \frac{10}{3} - \frac{5}{9} = \frac{30}{9} - \frac{5}{9} = \frac{25}{9} = 2\frac{7}{9} \)

б) \( \left(2\frac{1}{3} \cdot 1\frac{1}{7}\right)^3 \cdot \frac{2}{9} = \left(\frac{7}{3} \cdot \frac{8}{7}\right)^3 \cdot \frac{2}{9} = \left(\frac{8}{3}\right)^3 \cdot \frac{2}{9} = \frac{512}{27} \cdot \frac{2}{9} = \frac{1024}{243} \)

в) \( \frac{7}{11} \cdot \left(\left(\frac{3}{7}\right)^2 + \frac{5}{7}\right) = \frac{7}{11} \cdot \left(\frac{9}{49} + \frac{5}{7}\right) = \frac{7}{11} \cdot \left(\frac{9}{49} + \frac{35}{49}\right) = \frac{7}{11} \cdot \frac{44}{49} = \frac{1}{1} \cdot \frac{4}{7} = \frac{4}{7} \)

г) \( \left(\frac{7}{12} - \frac{3}{16} - \frac{5}{24}\right) + \left(\frac{1}{4}\right)^2 = \left(\frac{14}{24} - \frac{9}{48} - \frac{10}{48}\right) + \frac{1}{16} = \left(\frac{28}{48} - \frac{9}{48} - \frac{10}{48}\right) + \frac{1}{16} = \frac{9}{48} + \frac{1}{16} = \frac{3}{16} + \frac{1}{16} = \frac{4}{16} = \frac{1}{4} \)

Ответ: а) \(2\frac{7}{9}\); б) \(\frac{1024}{243}\); в) \(\frac{4}{7}\); г) \(\frac{1}{4}\).