Example

Solve for $w$: $\quad w^{1/4} = -5$

Solution

Let's solve this equation using two different strategies.

Approach #1: Rewrite with radicals...

The new equation is impossible because even-indexed radicals cannot be negative. There is no solution.

Approach #2: Undo with fractional exponents...

We really cannot use this strategy to do anything for this example. We must recognize at the start of the solution process that there actually is no solution. A $1/4$ power cannot be a negative number. There is no solution.