I'd say 7^(1/3) is illuminating in the sense that 1. Someone understanding this is more likely to understand the concept of inverse functions. 2. Someone unde

I'd say 7^(1/3) is illuminating in the sense that 1. Someone understanding this is more likely to understand the concept of inverse functions. 2. Someone understanding this is more likely to understand how to solve x^(3/5) = 7. And then more likely to understand how to solve x^(sqrt(2)) = 7. In a college algebra level type course the ultimate goal is not knowing how to solve x^3 = 27. The ultimate goal is to understand more complicated ideas. The reasoning displayed is a huge red flag. In college algebra a student presenting the solution given will very likely fail the course. That student needs help.