3.146 Вычислите: 1) 2\frac{1}{4} \cdot 2^3; 2) 3\frac{1}{5} : 2^4; 3) 4,42 + (2,5)^3; 4) 30 − (3,6)^2; 5) 3^3 \cdot (1\frac{1}{3})^2; 6) (3\frac{3}{4})^2 : (1\frac{1}{4})^3.

1)

$$2\frac{1}{4} \cdot 2^3 = \frac{9}{4} \cdot 8 = 9 \cdot 2 = 18$$

2)

$$3\frac{1}{5} : 2^4 = \frac{16}{5} : 16 = \frac{16}{5} \cdot \frac{1}{16} = \frac{1}{5} = 0,2$$

3)

$$4,42 + (2,5)^3 = 4,42 + 2,5 \cdot 2,5 \cdot 2,5 = 4,42 + 6,25 \cdot 2,5 = 4,42 + 15,625 = 20,045$$

4)

$$30 - (3,6)^2 = 30 - 3,6 \cdot 3,6 = 30 - 12,96 = 17,04$$

5)

$$3^3 \cdot (1\frac{1}{3})^2 = 27 \cdot (\frac{4}{3})^2 = 27 \cdot \frac{16}{9} = 3 \cdot 16 = 48$$

6)

$$(3\frac{3}{4})^2 : (1\frac{1}{4})^3 = (\frac{15}{4})^2 : (\frac{5}{4})^3 = \frac{225}{16} : \frac{125}{64} = \frac{225}{16} \cdot \frac{64}{125} = \frac{225}{1} \cdot \frac{4}{125} = \frac{900}{125} = \frac{36}{5} = 7,2$$

Ответ: 1) 18; 2) 0,2; 3) 20,045; 4) 17,04; 5) 48; 6) 7,2