Выполните действия: a) $$(2\frac{1}{2})^2 \cdot \frac{8}{15} - \frac{5}{9}$$ б) $$(2\frac{1}{3} \cdot 1\frac{2}{7})^3 \cdot \frac{2}{9}$$ в) \(\frac{7}{11} \cdot (\(\frac{3}{7}\)^2 + \(\frac{5}{7}\)) \(\div\) \(\frac{2}{7}\) г) \(\frac{7}{12} - \frac{3}{16} - \frac{5}{24}\) + \(\frac{1}{4}\)^2$$

Решение:

1. \((2\frac{1}{2})^2 = (\frac{5}{2})^2 = \frac{25}{4}\)
2. \(\frac{25}{4} \cdot \frac{8}{15} = \frac{5}{1} \cdot \frac{2}{3} = \frac{10}{3}\)
3. \(\frac{10}{3} - \frac{5}{9} = \frac{30 - 5}{9} = \frac{25}{9}\)
4. \(2\frac{1}{3} = \frac{7}{3}\); \(1\frac{2}{7} = \frac{9}{7}\)
5. \(\frac{7}{3} \cdot \frac{9}{7} = 3\)
6. \(3^3 = 27\)
7. \(27 \cdot \frac{2}{9} = 3 \cdot 2 = 6\)
8. \((\frac{3}{7})^2 = \frac{9}{49}\)
9. \(\frac{9}{49} + \frac{5}{7} = \frac{9 + 35}{49} = \frac{44}{49}\)
10. \(\frac{7}{11} \cdot \frac{44}{49} = \frac{1}{1} \cdot \frac{4}{7} = \frac{4}{7}\)
11. \(\frac{4}{7} \div \frac{2}{7} = \frac{4}{7} \cdot \frac{7}{2} = 2\)
12. \(\frac{7}{12} - \frac{3}{16} - \frac{5}{24} = \frac{14 - 9 - 10}{24} = \frac{-5}{24}\)
13. \((\frac{1}{4})^2 = \frac{1}{16}\)
14. \(\frac{-5}{24} + \frac{1}{16} = \frac{-10 + 3}{48} = \frac{-7}{48}\)

Ответ: а) \(\frac{25}{9}\); б) 6; в) 2; г) \(\frac{-7}{48}\).