57. Вычислить: 1) \(64^{\frac12}\); 2) \(27^{\frac13}\); 3) \(8^{\frac23}\); 4) \(81^{\frac34}\); 5) \(16^{-0.75}\); 6) \(9^{-1.5}\).

1. \(64^{\frac12}=\sqrt{64}=8\).
2. \(27^{\frac13}=\sqrt[3]{27}=3\).
3. \(8^{\frac23}=\left(\sqrt[3]{8}\right)^2=2^2=4\).
4. \(81^{\frac34}=\left(\sqrt[4]{81}\right)^3=3^3=27\).
5. \(16^{-0.75}=16^{-\frac34}=\frac{1}{16^{\frac34}}=\frac{1}{\left(\sqrt[4]{16}\right)^3}=\frac{1}{2^3}=\frac18\).
6. \(9^{-1.5}=9^{-\frac32}=\frac{1}{9^{\frac32}}=\frac{1}{\left(\sqrt{9}\right)^3}=\frac{1}{27}\).

Ответ: 1) 8; 2) 3; 3) 4; 4) 27; 5) \(\frac18\); 6) \(\frac1{27}\).