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Write problem as a single radical using the smallest possible root. 19

Write problem as a single radical using the smallest possible root. 19-example-1
User Ryrich
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Answer:


\sqrt[30]{r^(17)}

Step-by-step explanation:

Here, we want to simplify the given expression

Mathematically, we shall be using two indices rule as follows:


\begin{gathered} a^x* a^y\text{ = a}^(x+y) \\ \\ a^{(x)/(y)}\text{ = }\sqrt[y]{a^x} \end{gathered}

Applying these rules, we have:


\begin{gathered} \sqrt[5]{r^2}\text{ = r}^{(2)/(5)} \\ \sqrt[6]{r}\text{ = r}^{(1)/(6)} \end{gathered}

The product of the two will be:


r^{(2)/(5)+(1)/(6)}\text{ = r}^{(17)/(30)}\text{ = }\sqrt[30]{r^(17)}

User Lisle
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