5.470 Найдите значение выражения: а) 6/7 * 7/12 * 5/3; б) 3/4 * 10/13 * 39/40; в) 11 * 5/33 * 3/10; г) 3/4 * 4/5 * 5/6 * 12; д) (2/3)^2 + 13/21 * 7/26 - 5/18; е) (3/7 - 1/7)^2 * 49/16 + (1/2)^3.

1. а) $$\frac{6}{7} \cdot \frac{7}{12} \cdot \frac{5}{3} = \frac{6 \cdot 7 \cdot 5}{7 \cdot 12 \cdot 3} = \frac{1 \cdot 1 \cdot 5}{1 \cdot 2 \cdot 3} = \frac{5}{6}$$
2. б) $$\frac{3}{4} \cdot \frac{10}{13} \cdot \frac{39}{40} = \frac{3 \cdot 10 \cdot 39}{4 \cdot 13 \cdot 40} = \frac{3 \cdot 1 \cdot 3}{4 \cdot 1 \cdot 4} = \frac{9}{16}$$
3. в) $$11 \cdot \frac{5}{33} \cdot \frac{3}{10} = \frac{11 \cdot 5 \cdot 3}{33 \cdot 10} = \frac{1 \cdot 1 \cdot 1}{1 \cdot 2} = \frac{1}{2}$$
4. г) $$\frac{3}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} \cdot 12 = \frac{3 \cdot 4 \cdot 5 \cdot 12}{4 \cdot 5 \cdot 6} = \frac{3 \cdot 1 \cdot 1 \cdot 2}{1 \cdot 1 \cdot 1} = 6$$
5. д) $$\left(\frac{2}{3}\right)^2 + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18} = \frac{4}{9} + \frac{13 \cdot 7}{21 \cdot 26} - \frac{5}{18} = \frac{4}{9} + \frac{1 \cdot 1}{3 \cdot 2} - \frac{5}{18} = \frac{4}{9} + \frac{1}{6} - \frac{5}{18} = \frac{8}{18} + \frac{3}{18} - \frac{5}{18} = \frac{8+3-5}{18} = \frac{6}{18} = \frac{1}{3}$$
6. е) $$\left(\frac{3}{7} - \frac{1}{7}\right)^2 \cdot \frac{49}{16} + \left(\frac{1}{2}\right)^3 = \left(\frac{2}{7}\right)^2 \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{49} \cdot \frac{49}{16} + \frac{1}{8} = \frac{1}{4} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} = \frac{3}{8}$$

Ответ: а) 5/6; б) 9/16; в) 1/2; г) 6; д) 1/3; е) 3/8.