Electric Power in Frequency Domain
For any voltage signal that is connected to some impedance Z, there is a resulting current. The voltage may be arbitrary and even the impedance can be arbitrarily changing but the same rule applies for calculating power: -

Power equals voltage multiplied by current

And, in this case, the voltage and currents are instantaneous values rather than RMS values. This is the bottom line for power measurement when you can't use sine waves (or regular cyclic signals) and the load might be varying.

So, instantaneous power values (calculated from instantaneous voltage and instantaneous current values) are averaged to produce average power and, it is average power that is important (especially so because power companies bill you on average power consumption, amongst other things).