Im trying to either prove or disprove that if a and b are rational numbers, then a^b is also rational. I tried doing it with a contradiction, but i cant seem to correctly arrive at a solution. this is how i started the problem(adsbygoogle = window.adsbygoogle || []).push({});

defn of rational number: a,b = {m/n: m,n are all nonzero integers}

1. a^b is irrational (hypothesis/assumption)

2. b^b is irrational (from 1)

3. (m/n)^(m/n) (from defn. of rational number)

4. [m^(m/n)]/[(n^(m/n)] (algebra)

i'm stuck right here. i need to prove that an integer raised to a rational number is either rational or irrational. any inputs will be really helpful. thank you

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# Homework Help: Proving or Disproving rational raised to rational is rational number

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