$\begin{array}{l} \sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a\cdot b} \\ \sqrt[n]{a}:\sqrt[n]{b}=\sqrt[n]{\frac{a}{b}} \\ \sqrt[n]{\sqrt[m]{a}}=\sqrt[{mn}]{a} \\ \\ \textbf{Gegeben:} \\ {a=87 \qquad b=60 \qquad m=3 \qquad n=7}\\ \\ \textbf{Rechnung:} \\ \sqrt[7]{87} \cdot \sqrt[7]{60} = \sqrt[7]{87\cdot 60}= \sqrt[7]{5,22\cdot 10^{3}}=3,4 \\ \sqrt[7]{87}:\sqrt[7]{60}=\sqrt[7]{\frac{87}{60}} = \sqrt[7]{1\frac{9}{20}}=1,05 \\ \sqrt[7]{\sqrt[3]{87}}=\sqrt[{3\cdot 7}]{87}= \sqrt[21]{87}=1,24 \\ \end{array}$