  We study the collision frequencies of particles in the weakly and highly
ionized plasmas with the power-law q-distributions in nonextensive statistics.
We derive the average collision frequencies of neutral-neutral particle,
electron-neutral particle, ion-neutral particle, electron-electron, ion-ion and
electron-ion, respectively, in the q-distributed plasmas. We show that the
average collision frequencies depend strongly on the q-parameter in a complex
form and thus their properties are significantly different from that in
Maxwell-distributed plasmas. These new average collision frequencies are
important for us to study accurately the transport property in the complex
plasmas with non-Maxwell/power-law velocity distributions.
