3) Вычислить: 8^(1/3), 27^(2/3), 10000^(1/4), 32^(2/5), 32^(−3/5), (27/64)^(2/3).

1. \(8^{\frac13}=\sqrt[3]{8}=2\).
2. \(27^{\frac23}=\left(\sqrt[3]{27}\right)^2=3^2=9\).
3. \(10000^{\frac14}=\sqrt[4]{10000}=10\).
4. \(32^{\frac25}=\left(\sqrt[5]{32}\right)^2=2^2=4\).
5. \(32^{-\frac35}=\frac{1}{32^{\frac35}}=\frac{1}{\left(\sqrt[5]{32}\right)^3}=\frac{1}{2^3}=\frac18\).
6. \(\left(\frac{27}{64}\right)^{\frac23}=\left(\sqrt[3]{\frac{27}{64}}\right)^2=\left(\frac34\right)^2=\frac{9}{16}\).

Ответ: 2; 9; 10; 4; \(\frac18\); \(\frac{9}{16}\).