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Math Help - Prove or disprove that (a^b) is rational...

  1. #1
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    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!!
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  2. #2
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    Quote Originally Posted by collegestudent321 View Post
    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?
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  3. #3
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    ohhhhhhhhhh ok... so that means that its not true cuz a = 2 and b = 1/2 is a counterexample, right?????
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  4. #4
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    Quote Originally Posted by collegestudent321 View Post
    ohhhhhhhhhh ok... so that means that its not true cuz a = 2 and b = 1/2 is a counterexample, right?????
    Right.
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  5. #5
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    Awesome! Thank you!!!
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