A7 chord inversions
A7/C#, A7/E and A7/G are the first, second and third inversions of the A7. This means that the bass tone is shifting from A to C sharp, E or G.
A7/C#
A7/E
A7/G
Theory and information
All these chords consist of the notes A, C#, E, G. The difference is that the order of notes shifts. C# is the bass note in the first inversion, E is the bass note in the second inversion and G is the bass note in the third inversion.
Alternative fingerings
A7/C# can also be played as X42025. Notice that X42020 are not working since it miss the root note (although it may function as a rootless voicing, but can otherwise be regarded as a C#dim chord). A7/E can also be played as 002023, avoiding the E note tripling.
Movable shapes
Versions with movable barre shapes:
A7/C#: 9 10 11 9 10 9
A7/G: X10 11 12 11 12
Alternative chord names
A7/G is identical with A/G.
Try in a chord progression
Em9 - A7/E - F#m7