Вычислить (57-60). 2 57 1) 64: 2) 275; 3) 85; 4) 81; 5) 16-975; 6) 9-15 25 58 1) 25.27. 2) 57.57; 3) 9:9 (4) 4:45) (8) 2 2 33 33 591) 93.27; 2) 73.493 3) 144797 4) 150:6 95-275; 1-0,75 16 601) (금)~0.75+(); 2) (0.04)-1-(0.125)

Задание 57:

1. \[64^{\frac{1}{2}} = \sqrt{64} = 8\]

2. \[27^{\frac{2}{3}} = (27^{\frac{1}{3}})^2 = (\sqrt[3]{27})^2 = 3^2 = 9\]

3. \[8^{\frac{2}{3}} = (8^{\frac{1}{3}})^2 = (\sqrt[3]{8})^2 = 2^2 = 4\]

4. \[81^{\frac{3}{4}} = (81^{\frac{1}{4}})^3 = (\sqrt[4]{81})^3 = 3^3 = 27\]

5. \[16^{-0.75} = 16^{-\frac{3}{4}} = \frac{1}{16^{\frac{3}{4}}} = \frac{1}{(\sqrt[4]{16})^3} = \frac{1}{2^3} = \frac{1}{8} = 0.125\]

6. \[9^{-1.5} = 9^{-\frac{3}{2}} = \frac{1}{9^{\frac{3}{2}}} = \frac{1}{(\sqrt{9})^3} = \frac{1}{3^3} = \frac{1}{27}\]

Задание 58:

1. \[2^{\frac{4}{5}} \cdot 2^{\frac{11}{5}} = 2^{\frac{4}{5} + \frac{11}{5}} = 2^{\frac{15}{5}} = 2^3 = 8\]

2. \[5^{\frac{2}{7}} \cdot 5^{\frac{5}{7}} = 5^{\frac{2}{7} + \frac{5}{7}} = 5^{\frac{7}{7}} = 5^1 = 5\]

3. \[9^{\frac{3}{5}} : 9^{\frac{1}{6}} = 9^{\frac{3}{5} - \frac{1}{6}} = 9^{\frac{18}{30} - \frac{5}{30}} = 9^{\frac{13}{30}}\]

4. \[4^{\frac{1}{3}} : 4^{\frac{5}{6}} = 4^{\frac{1}{3} - \frac{5}{6}} = 4^{\frac{2}{6} - \frac{5}{6}} = 4^{-\frac{3}{6}} = 4^{-\frac{1}{2}} = \frac{1}{4^{\frac{1}{2}}} = \frac{1}{\sqrt{4}} = \frac{1}{2} = 0.5\]

5. \[(8^{\frac{1}{12}})^{-4} = 8^{\frac{1}{12} \cdot (-4)} = 8^{-\frac{4}{12}} = 8^{-\frac{1}{3}} = \frac{1}{8^{\frac{1}{3}}} = \frac{1}{\sqrt[3]{8}} = \frac{1}{2} = 0.5\]

Задание 59:

1. \[9^{\frac{2}{5}} \cdot 27^{\frac{2}{5}} = (3^2)^{\frac{2}{5}} \cdot (3^3)^{\frac{2}{5}} = 3^{\frac{4}{5}} \cdot 3^{\frac{6}{5}} = 3^{\frac{4}{5} + \frac{6}{5}} = 3^{\frac{10}{5}} = 3^2 = 9\]

2. \[7^{\frac{2}{3}} \cdot 49^{\frac{2}{3}} = 7^{\frac{2}{3}} \cdot (7^2)^{\frac{2}{3}} = 7^{\frac{2}{3}} \cdot 7^{\frac{4}{3}} = 7^{\frac{2}{3} + \frac{4}{3}} = 7^{\frac{6}{3}} = 7^2 = 49\]

3. \[144^{\frac{3}{4}} : 9^{\frac{3}{4}} = (144:9)^{\frac{3}{4}} = (16)^{\frac{3}{4}} = (2^4)^{\frac{3}{4}} = 2^3 = 8\]

4. \[150^{\frac{3}{2}} : 6^{\frac{3}{2}} = (150 : 6)^{\frac{3}{2}} = (25)^{\frac{3}{2}} = (5^2)^{\frac{3}{2}} = 5^3 = 125\]

Задание 60:

1. \[(\frac{1}{16})^{-0.75} + (\frac{1}{8})^{-\frac{4}{3}} = (\frac{1}{16})^{-\frac{3}{4}} + (\frac{1}{8})^{-\frac{4}{3}} = 16^{\frac{3}{4}} + 8^{\frac{4}{3}} = (2^4)^{\frac{3}{4}} + (2^3)^{\frac{4}{3}} = 2^3 + 2^4 = 8 + 16 = 24\]

2. \[(0.04)^{-1.5} - (0.125)^{-\frac{2}{3}} = (\frac{4}{100})^{-\frac{3}{2}} - (\frac{125}{1000})^{-\frac{2}{3}} = (\frac{1}{25})^{-\frac{3}{2}} - (\frac{1}{8})^{-\frac{2}{3}} = 25^{\frac{3}{2}} - 8^{\frac{2}{3}} = (5^2)^{\frac{3}{2}} - (2^3)^{\frac{2}{3}} = 5^3 - 2^2 = 125 - 4 = 121\]