Conjecture no. 24 On Transcendental Numbers 2

a^b is always transcendental when (a,b) are real transcendental numbers.

A transcendental number is a number that is not the solution of a polynomial with integer coefficients.

An example of a provably transcendental number follows.

One such number that is transcendental by this is e^pi.

The transcendence of e^pi was proven as a corollary of the Gelfond-Schneider Theorem so its transcendence has been established independently of this conjecture.

Also is the P-adic varient of this conjecture true?

https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_theorem

https://en.wikipedia.org/wiki/Gelfond%27s_constant

https://en.wikipedia.org/wiki/P-adic_number

As always I welcome the readers to prove or disprove this conjecture.

Thank You,

Nunghead