Question is pretty much explained in the title. My inclination is to say "yes", but I'm unsure.
Thanks in advance!
2026-03-29 12:41:10.1774788070
Is every rational number raised to a rational power an algebraic number?
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Yes. $\displaystyle \left( \frac{a}{b}\right) ^{\frac{p}{q}}$ is a root of $\displaystyle b^p x^q - a^p = 0$.