№14. Вычислить: 1) \(\sqrt[3]{10^6}\); 2) \(\sqrt[3]{3^{12}}\); 3) \(\sqrt[4]{\left(\frac12\right)^{12}}\); 4) \(\sqrt[4]{\left(\frac13\right)^{16}}\).

1. \(\sqrt[3]{10^6}=10^{6/3}=10^2=100\).
2. \(\sqrt[3]{3^{12}}=3^{12/3}=3^4=81\).
3. \(\sqrt[4]{\left(\frac12\right)^{12}}=\left(\frac12\right)^{12/4}=\left(\frac12\right)^3=\frac18\).
4. \(\sqrt[4]{\left(\frac13\right)^{16}}=\left(\frac13\right)^{16/4}=\left(\frac13\right)^4=\frac{1}{81}\).

Ответ: 1) 100; 2) 81; 3) \(\frac18\); 4) \(\frac{1}{81}\).