I think you have finished your proof.
"Prove or disprove that if a and b are rational numbers, then a^b is also rational."
a = s/r, b = c/d.
(s^(c/d)) / (r^(c/d))
Now I am back where I started. Both the numerator and denominator is a rational number raised to a rational number. I'm not even sure If I am taking the right approach. Please help, thank you.
If you're not getting anywhere with a proof, it might mean that you haven't hit on the right idea, or it could mean that there can be no proof because the statement is false. See if you can find a counterexample-maybe a certain integer* raised to the 1/2 power.
*You've at least proved something: if the statement is false, then there must be a counterexample with an integer as the base.
Looks like Prove It beat me to it, so I'll just add my favorite smiley to serve as my Q.E.D symbol.