871. Вычислите: 1) 32.1\frac{1}{6}; 2) 2\frac{2}{3} : 2^3; 3) (3,1)³ + 2,75; 4) 26 - (2,1)²; 5) (1\frac{1}{2})^2 \cdot 2^3; 6) (2\frac{2}{3})^3 : (\frac{2}{3})^2.

Решим примеры:

1. $$3^2 \cdot 1\frac{1}{6} = 9 \cdot \frac{7}{6} = \frac{9 \cdot 7}{6} = \frac{3 \cdot 7}{2} = \frac{21}{2} = 10,5$$
2. $$2\frac{2}{3} : 2^3 = \frac{8}{3} : 8 = \frac{8}{3} \cdot \frac{1}{8} = \frac{1}{3}$$
3. $$(3,1)^3 + 2,75 = 3,1 \cdot 3,1 \cdot 3,1 + 2,75 = 9,61 \cdot 3,1 + 2,75 = 29,791 + 2,75 = 32,541$$
4. $$26 - (2,1)^2 = 26 - 2,1 \cdot 2,1 = 26 - 4,41 = 21,59$$
5. $$(1\frac{1}{2})^2 \cdot 2^3 = (\frac{3}{2})^2 \cdot 8 = \frac{9}{4} \cdot 8 = \frac{9 \cdot 8}{4} = 9 \cdot 2 = 18$$
6. $$(2\frac{2}{3})^3 : (\frac{2}{3})^2 = (\frac{8}{3})^3 : (\frac{2}{3})^2 = \frac{8^3}{3^3} : \frac{2^2}{3^2} = \frac{8^3}{3^3} \cdot \frac{3^2}{2^2} = \frac{8^3}{3 \cdot 2^2} = \frac{512}{3 \cdot 4} = \frac{512}{12} = \frac{128}{3} = 42\frac{2}{3}$$

Ответ: 1) 10,5; 2) 1/3; 3) 32,541; 4) 21,59; 5) 18; 6) 42 2/3