Example

Solve for $r$: $\quad r^{1/4}=3$

Solution

Let's solve this equation using two different strategies.

Approach #1: Rewrite with radicals...

We must check our solution in the original equation, and it works. There is a single solution, $r=81$.

Approach #2: Undo with fractional exponents...

To undo a $1/4$ power, we use a $4/1$ power.

With this approach, we must also check our solution, and as we know, it works!