Multiplication of average voltage and current?
Multiplication of Vrms and Irms gives average power into a resistive load only. Into other loads which result in out of phase waveforms, capacitive, inductive, rectifier for instance, the result is not average power.

If you multiply Iavg by Vavg, the caveats are similar. For well behaved waveforms like DC, the result is average power. It's easy however to construct other waveforms into other loads for which it's not average power.

In all cases, you get average power from averaging the product of the instantaneous voltage and the instantaneous current. In some well behaved cases, you can take short-cuts.