Вычислите: 1) \(4^3\); 2) \(\left(\frac{2}{3}\right)^3\); 3) \(2^{-4}\); 4) \(\left(\frac{2}{5}\right)^{-2}\); 5) \((\sqrt{2})^8\); 6) \(\frac{1}{64^{\frac{1}{2}}}\); 7) \(\left(\frac{1}{9}\right)^{-\frac{1}{2}}\); 8) \(\frac{1}{16^{\frac{1}{4}}}\); 9) \(\frac{-3}{4^{-\frac{1}{2}}}\); 10) \((\sqrt{27})^{\frac{2}{3}}\).

1. \(4^3=64\).
2. \(\left(\frac{2}{3}\right)^3=\frac{2^3}{3^3}=\frac{8}{27}\).
3. \(2^{-4}=\frac{1}{2^4}=\frac{1}{16}\).
4. \(\left(\frac{2}{5}\right)^{-2}=\left(\frac{5}{2}\right)^2=\frac{25}{4}\).
5. \((\sqrt{2})^8=(2^{\frac12})^8=2^4=16\).
6. \(\frac{1}{64^{\frac12}}=\frac{1}{\sqrt{64}}=\frac18\).
7. \(\left(\frac19\right)^{-\frac12}=\frac{1}{\sqrt{\frac19}}=3\).
8. \(\frac{1}{16^{\frac14}}=\frac{1}{\sqrt[4]{16}}=\frac12\).
9. \(\frac{-3}{4^{-\frac12}}=\frac{-3}{\frac12}=-6\).
10. \((\sqrt{27})^{\frac23}=((27)^{\frac12})^{\frac23}=27^{\frac13}=3\).

Ответ: 1) 64; 2) \(\frac{8}{27}\); 3) \(\frac{1}{16}\); 4) \(\frac{25}{4}\); 5) 16; 6) \(\frac18\); 7) 3; 8) \(\frac12\); 9) −6; 10) 3.