Pretty much a newbie here, but would like to understand a pretty basic concept.
We all know that a quick and dirty way of calculating signal power of a part of a discrete sampled system (such as audio signals) is the age-old power formula for RMS power, where we simply break the signal into chunks of N samples and sum the squares of the amplitudes, then divide by the number of samples
$$ P_\mathrm{x} = \dfrac{1}{N}\sum_{n=1}^{N}|x[n]|^2 $$
So let's say I have 10ms samples of two completely uncorrelated signals at 48khz (480 samples), and I have calculated the RMS power of these samples using the above formula and have come up with P1 and P2, the power of my small segment of each signal.
Then if I sum the two signals (simple software mixer function), what is the resultant power of the two summed signals? Is it simply P1 + P2?
If so, do I simply keep going? So if I had four signals with P1, P2, P3 and P4, if I sum all four of them together, is the resultant RMS power P1+P2+P3+P4?