Question

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

Answer 1

`\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)}`