2.310 Вычислите: a) \frac{4}{9} \cdot (\frac{3}{14} \cdot 2\frac{4}{5})^2 ; b) ((\frac{2}{3})^3 + \frac{5}{9}) \cdot \frac{9}{11}; в) (2\frac{1}{2} - \frac{11}{14}) \cdot (1\frac{4}{9} + 2\frac{5}{6} - 2\frac{2}{3})

a) Вычислим:

1. $$2\frac{4}{5} = \frac{2 \cdot 5 + 4}{5} = \frac{14}{5}$$
2. $$(\frac{3}{14} \cdot \frac{14}{5})^2 = (\frac{3 \cdot 14}{14 \cdot 5})^2 = (\frac{3}{5})^2 = \frac{3^2}{5^2} = \frac{9}{25}$$
3. $$\frac{4}{9} \cdot \frac{9}{25} = \frac{4 \cdot 9}{9 \cdot 25} = \frac{4}{25}$$

Ответ: \frac{4}{25}

б) Вычислим:

1. $$(\frac{2}{3})^3 = \frac{2^3}{3^3} = \frac{8}{27}$$
2. $$\frac{8}{27} + \frac{5}{9} = \frac{8}{27} + \frac{5 \cdot 3}{9 \cdot 3} = \frac{8}{27} + \frac{15}{27} = \frac{8 + 15}{27} = \frac{23}{27}$$
3. $$\frac{23}{27} \cdot \frac{9}{11} = \frac{23 \cdot 9}{27 \cdot 11} = \frac{23 \cdot 1}{3 \cdot 11} = \frac{23}{33}$$

Ответ: \frac{23}{33}

в) Вычислим:

1. $$2\frac{1}{2} = \frac{2 \cdot 2 + 1}{2} = \frac{5}{2}$$
2. $$1\frac{4}{9} = \frac{1 \cdot 9 + 4}{9} = \frac{13}{9}$$
3. $$2\frac{5}{6} = \frac{2 \cdot 6 + 5}{6} = \frac{17}{6}$$
4. $$2\frac{2}{3} = \frac{2 \cdot 3 + 2}{3} = \frac{8}{3}$$
5. $$\frac{5}{2} - \frac{11}{14} = \frac{5 \cdot 7}{2 \cdot 7} - \frac{11}{14} = \frac{35}{14} - \frac{11}{14} = \frac{35 - 11}{14} = \frac{24}{14} = \frac{12}{7}$$
6. $$\frac{13}{9} + \frac{17}{6} - \frac{8}{3} = \frac{13 \cdot 2}{9 \cdot 2} + \frac{17 \cdot 3}{6 \cdot 3} - \frac{8 \cdot 6}{3 \cdot 6} = \frac{26}{18} + \frac{51}{18} - \frac{48}{18} = \frac{26 + 51 - 48}{18} = \frac{29}{18}$$
7. $$\frac{12}{7} \cdot \frac{29}{18} = \frac{12 \cdot 29}{7 \cdot 18} = \frac{2 \cdot 29}{7 \cdot 3} = \frac{58}{21} = 2\frac{16}{21}$$

Ответ: 2\frac{16}{21}