$\begin{array}{l} \sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a\cdot b} \\ \sqrt[n]{a}:\sqrt[n]{b}=\sqrt[n]{\frac{a}{b}} \\ \sqrt[n]{\sqrt[m]{a}}=\sqrt[{mn}]{a} \\ \\ \textbf{Gegeben:} \\ {a=49 \qquad b=12 \qquad m=2 \qquad n=3}\\ \\ \textbf{Rechnung:} \\ \sqrt[3]{49} \cdot \sqrt[3]{12} = \sqrt[3]{49\cdot 12}= \sqrt[3]{588}=8,38 \\ \sqrt[3]{49}:\sqrt[3]{12}=\sqrt[3]{\frac{49}{12}} = \sqrt[3]{4\frac{1}{12}}=1,6 \\ \sqrt[3]{\sqrt[2]{49}}=\sqrt[{2\cdot 3}]{49}= \sqrt[6]{49}=1,91 \\ \end{array}$