I've been puzzling over this question about number theory.
Ignoring complex numbers, and working only with positive numbers:
Can one say that a positive rational number raised to a positive irrational exponent is always irrational?
Thank you, Hein
2026-03-27 14:21:35.1774621295
Positive rational raised to positive irrational is always irrational?
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No. For example $x:=\log_2(3)$ is irrational but $2^x=3$.