33. 1) √[3](10⁶); 2) √[3](3¹²); 3) √[4]((1/2)¹²); 4) √[4]((1/3)¹⁶).

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

Ответ: 1) 100; 2) 81; 3) 1/8; 4) 1/81.