5.471 Выполните действия: a) (4/9 + 2/9) · 9/13; б) (2/3 · 3/8) : (9/11 - 4/11) · 11/5; в) (3/7 - 1/7)² · 49/16 + (1/2)³; г) (2/3)² + 13/21 · 7/26 - 5/18. д) (3/7 - 1/7)² · 49/16 + (1/2)³.

a) $$\left( \frac{4}{9} + \frac{2}{9} \right) \cdot \frac{9}{13} = \frac{4 + 2}{9} \cdot \frac{9}{13} = \frac{6}{9} \cdot \frac{9}{13} = \frac{6 \cdot 9}{9 \cdot 13} = \frac{54}{117} = \frac{6}{13}$$.

б) $$\left( \frac{2}{3} \cdot \frac{3}{8} \right) : \left( \frac{9}{11} - \frac{4}{11} \right) \cdot \frac{11}{5} = \left( \frac{2 \cdot 3}{3 \cdot 8} \right) : \left( \frac{9-4}{11} \right) \cdot \frac{11}{5} = \frac{6}{24} : \frac{5}{11} \cdot \frac{11}{5} = \frac{1}{4} : \frac{5}{11} \cdot \frac{11}{5} = \frac{1}{4} \cdot \frac{11}{5} \cdot \frac{11}{5} = \frac{1}{4} \cdot 1 = \frac{1}{4}$$.

в) $$\left( \frac{3}{7} - \frac{1}{7} \right)^2 \cdot \frac{49}{16} + \left( \frac{1}{2} \right)^3 = \left( \frac{3 - 1}{7} \right)^2 \cdot \frac{49}{16} + \frac{1}{8} = \left( \frac{2}{7} \right)^2 \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{49} \cdot \frac{49}{16} + \frac{1}{8} = \frac{4 \cdot 49}{49 \cdot 16} + \frac{1}{8} = \frac{1}{4} + \frac{1}{8} = \frac{2 + 1}{8} = \frac{3}{8}$$.

г) $$\left( \frac{2}{3} \right)^2 + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18} = \frac{4}{9} + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18} = \frac{4}{9} + \frac{13 \cdot 7}{21 \cdot 26} - \frac{5}{18} = \frac{4}{9} + \frac{1}{6} - \frac{5}{18} = \frac{8 + 3 - 5}{18} = \frac{6}{18} = \frac{1}{3}$$.

д) $$\left( \frac{3}{7} - \frac{1}{7} \right)^2 \cdot \frac{49}{16} + \left( \frac{1}{2} \right)^3 = \left( \frac{3 - 1}{7} \right)^2 \cdot \frac{49}{16} + \frac{1}{8} = \left( \frac{2}{7} \right)^2 \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{49} \cdot \frac{49}{16} + \frac{1}{8} = \frac{4 \cdot 49}{49 \cdot 16} + \frac{1}{8} = \frac{1}{4} + \frac{1}{8} = \frac{2 + 1}{8} = \frac{3}{8}$$.

Ответ: а) $$\frac{6}{13}$$; б) $$\frac{1}{4}$$; в) $$\frac{3}{8}$$; г) $$\frac{1}{3}$$; д) $$\frac{3}{8}$$