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

1. ## 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!!

2. 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?

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

4. 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.

5. Awesome! Thank you!!!

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### if a and b are rational numbers

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