How to prove that the power

glycleWogry

glycleWogry

Answered question

2022-06-07

How to prove that the power b n is an irrational number, where b is an integer greater than 1 and n is an irrational number?

Answer & Explanation

alisonhleel3

alisonhleel3

Beginner2022-06-08Added 23 answers

The Gelfond-Schneider theorem shows that if you assume that n is algebraic, then b n is indeed irrational, in fact transcendental! You can even take b to be algebraic.
So we can ask whether there's an easy proof that b n is irrational for b integral and n an algebraic irrational.

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