In course of reading Real Exponentiation from Analysis I: Terence Tao, I noted that the author did not define $0^c$ where $c>0$, thought he defined $0^0$ and $x^c$ for all $x>0,\ c\in\mathbb{R}$. However the wikipedia article gives definition of $0^c$ for $c>0$.
Why didn't Tao define $0^c$ for $c>0?$ Is there any text that covers such case?
N.B. Even in this text: springer.com/in/book/9781493927654 authors did the same.