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

1. \(\sqrt[3]{10^6}=\sqrt[3]{(10^2)^3}=10^2=100\).
2. \(\sqrt[3]{3^{12}}=\sqrt[3]{(3^4)^3}=3^4=81\).
3. \(\sqrt[4]{\left(\frac{1}{12}\right)^{12}}=\sqrt[4]{\left(\left(\frac{1}{12}\right)^3\right)^4}=\left(\frac{1}{12}\right)^3=\frac{1}{1728}\).
4. \(\sqrt[4]{\left(\frac{1}{3}\right)^{16}}=\sqrt[4]{\left(\left(\frac{1}{3}\right)^4\right)^4}=\left(\frac{1}{3}\right)^4=\frac{1}{81}\).

Ответ: 1) 100; 2) 81; 3) \(\frac{1}{1728}\); 4) \(\frac{1}{81}\).