Couple of problems i can't think through looking for some help...

Prove there exists a rational number a and an irrational number b such that a^b is irrational.

I was thinking that I could prove they were both irrational, taking square root two^square root two as A and square root two as B and it works. can't put my finger on this one.

Last one disprove statement there is a real number x such that x^6+x^4+1=2x^2.

Thank you for any help

Tonio