Trouble with Cube Roots Evaluation

I put together a template for solving radical equations and overall it had been working great. Now that I tried a different problem I noticed errors, but only on some steps of the solving process.

I have experienced similar issues with rational exponents when the fractions (or their reciprocals, since we are solving) are non-terminating. Evaluating 8^(1/3) gives an answer of 2, while evaluating x^(1/3) for when x is 8, does not. The latter seems to be calculating 1/3 before raising the 8 to that power.