2.310 Вычислите: a) 4/9 * (3 3/14 * 2 4/5) ^2 ; б) ((2/3)^3 + 5/9) * 9/11 ; B) (2 1/2 - 11/14) * (

a) Вычислим:

$$3 \frac{3}{14} = \frac{3 \cdot 14 + 3}{14} = \frac{42 + 3}{14} = \frac{45}{14}$$

$$2 \frac{4}{5} = \frac{2 \cdot 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5}$$

Тогда:

$$\frac{45}{14} \cdot \frac{14}{5} = \frac{45 \cdot 14}{14 \cdot 5} = \frac{45}{5} = 9$$

$$9^2 = 81$$

$$\frac{4}{9} \cdot 81 = \frac{4 \cdot 81}{9} = 4 \cdot 9 = 36$$

Ответ: 36

б) Вычислим:

$$\left( \frac{2}{3} \right)^3 = \frac{2^3}{3^3} = \frac{8}{27}$$

$$\frac{8}{27} + \frac{5}{9} = \frac{8}{27} + \frac{5 \cdot 3}{9 \cdot 3} = \frac{8}{27} + \frac{15}{27} = \frac{8 + 15}{27} = \frac{23}{27}$$

$$\frac{23}{27} \cdot \frac{9}{11} = \frac{23 \cdot 9}{27 \cdot 11} = \frac{23 \cdot 1}{3 \cdot 11} = \frac{23}{33}$$

Ответ: 23/33

в) Вычислим:

$$2 \frac{1}{2} = \frac{2 \cdot 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$$

$$\frac{5}{2} - \frac{11}{14} = \frac{5 \cdot 7}{2 \cdot 7} - \frac{11}{14} = \frac{35}{14} - \frac{11}{14} = \frac{35 - 11}{14} = \frac{24}{14} = \frac{12}{7} = 1 \frac{5}{7}$$

Ответ: 1 5/7