Power chords come in very handy if you're looking for an unobtrusive rhythm part. You often hear a percussive, muted guitar, steadily chunking away, especially in pop music. That's usually done using power chords. The root and fifth are common to both major and minor chords, so power chords apply to either. All you need to do is keep track of the roots (the letters) of the chord progression and play the power chord. But, it's important to remember that just because you're playing a power chord, there is in fact a real chord (as in 'major' or 'minor') behind it all, in other words, power chords are just stripped down major or minor chords, stripped of their third.
Power chords won't work against augmented or diminished chords because in those two cases, the 5 is altered. If those chord do appear in the progression and you want to keep that sound going, you'll need to sharp the 5 for the augmented and flat it for the diminished.
Power chords are no more 'powerful' than ordinary chords. I'm not sure where the term came from, but 'power-chords' aren't really even chords.
As we have learned, a minimum of three different tones (Root-Third-Fifth) is required to qualify as a chord. Power chords have only two:
What's missing is the Third, the 3. Since the 3 determines the major/minor quality, power-chords are neutral in that respect. When I first started playing, no one ever used the term power chords. It was when distortion and overdrive became common in rock music that players began leaving the 3 out of chords.
The sound of a normal major or minor chord gets very blurred out using distortion. So power chords are not really chords, they're intervals, although the way most people play them and the way they're shown below, they do in fact use three tones: two roots and a fifth. You can also just play them as two-note shapes.
This is the "E form' power chord because it's a cut down open E chord shape. Move this little shape up or down the fretboard. Many players leave out the top root note and just play the two bass strings.
This is the "A form' power chord because it's a cut down open A chord shape. This little shape is also movable. Once again, you can just play a root and a fifth (strings 5-4) but it will sound fuller if you double up the root as shown in the image.
You can see by those red crosses that a lot of muting is necessary, or careful picking/strumming, in order to avoid playing those strings. The E form is the easiest since you don't have to worry about muting the thick string, but if you run out of fingerboard, you will have to use the A form for some chords. As always, the root names the chord, so the best way to deal with these is to think of the full barre shapes/positions and then leave out the appropriate strings.