Thread: Prove or disprove that (a^b) is rational...

Hey guys,
I'm stuck on a problem that I thought would be easy. It goes like this:

Prove or disprove that if a and b are rational numbers, then (a^b) is also rational.

I thought I could do it by using proof by cases in which I changed the values of a and b with rational and irrational numbers, but obviously that didn't work because you can't prove EVERY case by doing this. I don't know what to do now, so ANY help would REALLY help. Thanks!!

Originally Posted by collegestudent321

Hey guys,
I'm stuck on a problem that I thought would be easy. It goes like this:

Prove or disprove that if a and b are rational numbers, then (a^b) is also rational.

I thought I could do it by using proof by cases in which I changed the values of a and b with rational and irrational numbers, but obviously that didn't work because you can't prove EVERY case by doing this. I don't know what to do now, so ANY help would REALLY help. Thanks!!

What if a = 2 and b = 1/2, for example?

ohhhhhhhhhh ok... so that means that its not true cuz a = 2 and b = 1/2 is a counterexample, right?????

Originally Posted by collegestudent321

ohhhhhhhhhh ok... so that means that its not true cuz a = 2 and b = 1/2 is a counterexample, right?????

Right.

Awesome! Thank you!!!