Rational Roots Theorem corollary and piano tuning: $\big(\frac{a}{b}\big)^n \neq 2$

Question

I'm trying to understand why pianos "can't be tuned" and am looking for a proof of a corollary of the rational roots theorem found here (looking for proof not by contradiction): https://youtu.be/1Hqm0dYKUx4?t=171

It's stated:

For any integers $a, b$ and $n$ with $n > 1$ then $\big(\frac{a}{b}\big)^n \neq 2$