## How do i prove or disprove the following statement:

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
veryhappyguy
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### How do i prove or disprove the following statement:

There exist positive irrational numbers a and b such that a^b is rational.

My first guess would be that the statement is false, but I do not know how to disprove it. I suck with irrationals
Can anyone help me??

maggiemagnet
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### Re: How do i prove or disprove the following statement:

Can you use something like $\left(2^{\frac{1}{2\pi}}\right)^{2\pi}\, ?$

veryhappyguy
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Joined: Fri Feb 26, 2010 5:09 am
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### Re: How do i prove or disprove the following statement:

I'm not sure but 2 is not irrational and the statement says the base and exponent are irrational.

maggiemagnet
Posts: 358
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### Re: How do i prove or disprove the following statement:

Is $2^{\frac{1}{2 \pi}}$ rational or irrational?