Вычислите: ∛125; ∛0,064; ⁴√0,0001; ⁴√81; ⁵√(−32); ⁷√(−128); ∛(3 3/8); ∛(1 91/125); ⁵√8 · ⁵√4; ∛25 · ∛5; ∛(9 · 24); ⁵√(48 · 162); ⁵√(6¹⁰ : (1/6)¹⁵); ⁷√(3²¹ · (1/3)¹⁴); ∛625 / ∛5; ⁷√2 / ⁷√256.

1. \(\sqrt[3]{125}=\sqrt[3]{5^3}=5\).
2. \(\sqrt[3]{0.064}=\sqrt[3]{0.4^3}=0.4\).
3. \(\sqrt[4]{0.0001}=\sqrt[4]{0.1^4}=0.1\).
4. \(\sqrt[4]{81}=\sqrt[4]{3^4}=3\).
5. \(\sqrt[5]{-32}=\sqrt[5]{(-2)^5}=-2\).
6. \(\sqrt[7]{-128}=\sqrt[7]{(-2)^7}=-2\).
7. \(\sqrt[3]{3\frac{3}{8}}=\sqrt[3]{\frac{27}{8}}=\frac{3}{2}\).
8. \(\sqrt[3]{1\frac{91}{125}}=\sqrt[3]{\frac{216}{125}}=\frac{6}{5}=1\frac{1}{5}\).
9. \(\sqrt[5]{8}\cdot\sqrt[5]{4}=\sqrt[5]{32}=2\).
10. \(\sqrt[3]{25}\cdot\sqrt[3]{5}=\sqrt[3]{125}=5\).
11. \(\sqrt[3]{9\cdot24}=\sqrt[3]{216}=6\).
12. \(\sqrt[5]{48\cdot162}=\sqrt[5]{7776}=6\).
13. \(\sqrt[5]{6^{10}:\left(\frac{1}{6}\right)^{15}}=\sqrt[5]{6^{10}:6^{-15}}=\sqrt[5]{6^{25}}=6^5=7776\).
14. \(\sqrt[7]{3^{21}\cdot\left(\frac{1}{3}\right)^{14}}=\sqrt[7]{3^{21}\cdot3^{-14}}=\sqrt[7]{3^7}=3\).
15. \(\frac{\sqrt[3]{625}}{\sqrt[3]{5}}=\sqrt[3]{\frac{625}{5}}=\sqrt[3]{125}=5\).
16. \(\frac{\sqrt[7]{2}}{\sqrt[7]{256}}=\sqrt[7]{\frac{2}{256}}=\sqrt[7]{\frac{1}{128}}=\frac{1}{2}\).

Ответ: 5; 0.4; 0.1; 3; −2; −2; \(\frac{3}{2}\); \(1\frac{1}{5}\); 2; 5; 6; 6; 7776; 3; 5; \(\frac{1}{2}\).