The Purplemath Forums

by **veryhappyguy** on Fri Feb 26, 2010 5:13 am

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??

**Sponsor**

by **maggiemagnet** on Fri Feb 26, 2010 1:29 pm

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

by **veryhappyguy** on Fri Feb 26, 2010 5:43 pm

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

by **maggiemagnet** on Sat Feb 27, 2010 12:53 pm

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

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