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