  The Arakelov-Zhang pairing $\langle\psi,\phi\rangle$ is a measure of the
"dynamical distance" between two rational maps $\psi$ and $\phi$ defined over a
number field $K$. It is defined in terms of local integrals on Berkovich space
at each completion of $K$. We obtain a simple expression for the important case
of the pairing with a power map, written in terms of integrals over Julia sets.
Under certain disjointness conditions on Julia sets, our expression simplifies
to a single canonical height term; in general, this term is a lower bound. As
applications of our method, we give bounds on the difference between the
canonical height $h_\phi$ and the standard Weil height $h$, and we prove a
rigidity statement about polynomials that satisfy a strong form of good
reduction.
