Zu b ∈ R + {\displaystyle {}b\in \mathbb {R} _{+}} und q ∈ Q {\displaystyle {}q\in \mathbb {Q} } mit q = r s {\displaystyle {}q={\frac {r}{s}}} ( s > 0 {\displaystyle {}s>0} ) setzt man
![{\displaystyle {}b^{q}=b^{\frac {r}{s}}:={\sqrt[{s}]{b^{r}}}\,.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2e0433d25f5086d586f1bb60e11b2868125dc90)