57. Вычислите: 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. \(16^{-0,75}=16^{-\frac34}=\dfrac1{16^{\frac34}}=\dfrac1{(\sqrt[4]{16})^3}=\dfrac1{2^3}=\dfrac18\).
6. \(9^{-1,5}=9^{-\frac32}=\dfrac1{9^{\frac32}}=\dfrac1{(\sqrt9)^3}=\dfrac1{27}\).

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