29 1) \(\sqrt[3]{10^6}\); 2) \(\sqrt[3]{3^{12}}\); 3) \(\sqrt[4]{(\frac{1}{2})^{12}}\); 4) \(\sqrt[4]{(\frac{1}{3})^{16}}.\)

Решение:

1. \(\sqrt[3]{10^6} = 10^{6/3} = 10^2 = 100\)
2. \(\sqrt[3]{3^{12}} = 3^{12/3} = 3^4 = 81\)
3. \(\sqrt[4]{(\frac{1}{2})^{12}} = (\frac{1}{2})^{12/4} = (\frac{1}{2})^3 = \frac{1^3}{2^3} = \frac{1}{8}\)
4. \(\sqrt[4]{(\frac{1}{3})^{16}} = (\frac{1}{3})^{16/4} = (\frac{1}{3})^4 = \frac{1^4}{3^4} = \frac{1}{81}\)

Ответ: 1) 100; 2) 81; 3) \(\frac{1}{8}\); 4) \(\frac{1}{81}\).