$\begin{array}{l} \sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a\cdot b} \\ \sqrt[n]{a}:\sqrt[n]{b}=\sqrt[n]{\frac{a}{b}} \\ \sqrt[n]{\sqrt[m]{a}}=\sqrt[{mn}]{a} \\ \\ \textbf{Gegeben:} \\ {a=2 \qquad b=63 \qquad m=4 \qquad n=3}\\ \\ \textbf{Rechnung:} \\ \sqrt[3]{2} \cdot \sqrt[3]{63} = \sqrt[3]{2\cdot 63}= \sqrt[3]{126}=5,01 \\ \sqrt[3]{2}:\sqrt[3]{63}=\sqrt[3]{\frac{2}{63}} = \sqrt[3]{\frac{2}{63}}=0,317 \\ \sqrt[3]{\sqrt[4]{2}}=\sqrt[{4\cdot 3}]{2}= \sqrt[12]{2}=1,06 \\ \end{array}$