47. Вычислите:

Решение:

1. \( 3^2 \cdot 1\frac{1}{6} = 9 \cdot \frac{7}{6} = \frac{63}{6} = 10\frac{3}{6} = 10\frac{1}{2} \)
2. \( 2\frac{2}{3} : 2\frac{1}{3} = \frac{8}{3} : \frac{7}{3} = \frac{8}{3} \cdot \frac{3}{7} = \frac{8}{7} = 1\frac{1}{7} \)
3. \( (3,1)^3 + 2,75 \)
4. \( 26 - (2,1)^2 = 26 - 4,41 = 21,59 \)
5. \( \left(1\frac{1}{2}\right)^2 \cdot 2^3 = \left(\frac{3}{2}\right)^2 \cdot 8 = \frac{9}{4} \cdot 8 = 18 \)
6. \( \left(2\frac{2}{3}\right) : \left(\frac{2}{3}\right)^2 = \frac{8}{3} : \frac{4}{9} = \frac{8}{3} \cdot \frac{9}{4} = 6 \)

Ответ: 1) \(10\frac{1}{2}\); 2) \(1\frac{1}{7}\); 3) \( (3,1)^3 + 2,75 \); 4) 21,59; 5) 18; 6) 6.