Roderick said

RMS values of the current and voltage are used to calculate the mean (or
average) value of the power, because these values of voltage and current are
equivalent to the DC values that would supply energy at the same rate, so
"mean
power level" is the quantity that should really be specified.

Yes. If you square the root of the mean square you obviously get the mean
square. Since the square is proportional to power, you get mean power.

There is real and meaningful confusion in this RMS power nonsense. Pure
inductors and capacitors dissipate no power, although they may have voltage
across them, and current through them, simultaneously. This is possible because
positive and negative power cancels. RMS power would not cancel, because it
would always be positive. Hence it is not a trivial confusion. It is indicative
of a serious lack of understanding of basic essentials.

My first question in the hifi shop is always "what kind of power is that?" If
man says "RMS" I walk out. Hence I now have to make all my own hifi.

cheers, Ian