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

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.

### 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??
veryhappyguy

Posts: 2
Joined: Fri Feb 26, 2010 5:09 am

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

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

maggiemagnet

Posts: 289
Joined: Mon Dec 08, 2008 12:32 am

### 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.
veryhappyguy

Posts: 2
Joined: Fri Feb 26, 2010 5:09 am

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

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

maggiemagnet

Posts: 289
Joined: Mon Dec 08, 2008 12:32 am