Fifth chords or fifth chord dyads are often referred to as “power chords” and annotated with the chord’s root and the fifth – F5 (these should not be considered or mistaken as dominant chords). Fifth chords only contain the root and the fifth, though they are often doubled with a higher octave of the root (R-P5-8th).
Technically, these are not chords because they don’t contain three different intervals. However, these are undoubtedly the most common chords in contemporary rock.
Inverted chords are simply chords that have been “rearranged”. You will often see something like D/F# when looking at a song transcription. All that the slash means is the F# is being used as a bass note. Since a D Major contains an F# (D-F#-A), the F3 is being substituted as the bass note instead of D.
To form an inversion is to displace the root with one of the intervals as the bass note and likewise, displace the remaining intervals. For instance, displacing the root to the third’s position, the third to the fifth’s position, the fifth to the seventh’s position, and the seventh to the root’s position. If you continue this pattern, you will get all the possible inversions for that chord (i.e. the root will be displaced to all the other positions until it ends up right back in its original position).
Inversions are found throughout blues, jazz, and rock. Perhaps the most common occurrence of inversions are found in rock. Many rock guitarists play fifth chord dyads, with the fifth acting as the bass note, doubled with the second octave of the root (8th). Instead of utilizing the root as the bass note, coupled with the perfect fifth, and an octave of the root (R-P5-8th), many guitarists will invert the chord, displacing the fifth to the bass note, incorporated with a higher octave of the root (P5- 8th). Be careful to label these as inversions, as they may actually be some type of fourth chord dyad or quartal chord (e.g. Deep Purple’s Smoke on the Water).