Example

Solve for $u$: $\quad (6u+4)^{1/3} + 3 = 7$

Solution

In order to use either one of our strategies, we must first isolate the expression with the fractional exponent.

Now let's solve this equation using approach #1. We rewrite the equation in radical form and solve.

We must now check our solution in the original equation:

It checks outs. The single solution is $u=10$.