An operator \(A\) is called an abstract potential if the resolvent set of \(A\) contains an open right half plane and if there is a constant \(a>0\) such that the function \((\text{Re}\cdot -a)(\cdot I-A)^{-1}\) is bounded on the set \(\mathbb C_a:=\{\lambda\in\mathbb C\mid \text{ Re}\lambda >a\}\). The main result of this paper is: Every abstract potential satisfies \(\| (\text{Re}\lambda -a)^n(\cdot I-A)^{-n}\| < Men\) for \(\lambda \in \mathbb C_a\) and every \(n\in \mathbb N\). Here \(M\) is the bound of \((\text{Re}\cdot -a)(\cdot I-A)^{-1}\) on \(\mathbb C_a\).