Answer:
[tex]\sqrt[30]{r^{17}}[/tex]
Explanation:
Here, we want to simplify the given expression
Mathematically, we shall be using two indices rule as follows:
[tex]\begin{gathered} a^x\times a^y\text{ = a}^{x+y} \\ \\ a^{\frac{x}{y}}\text{ = }\sqrt[y]{a^x} \end{gathered}[/tex]
Applying these rules, we have:
[tex]\begin{gathered} \sqrt[5]{r^2}\text{ = r}^{\frac{2}{5}} \\ \sqrt[6]{r}\text{ = r}^{\frac{1}{6}} \end{gathered}[/tex]
The product of the two will be:
[tex]r^{\frac{2}{5}+\frac{1}{6}}\text{ = r}^{\frac{17}{30}}\text{ = }\sqrt[30]{r^{17}}[/tex]
