If you press the tablet Volume - (Minus) button to completely lower the tablet volume, you will completely mute the tablet.
NOTE: Muting the tablet volume in this manner will also mute the Notification sounds.
You will find that while in this muted state, moving the touch-screen slider button will not affect the volume levels.
To take the tablet out of this muted state and allow the touch-screen slider buttons to again function to adjust the volume, press the Volume +(Plus) button twice.
Once the tablet is out of the muted state, you will again be able to use the touch-screen slider to adjust the volume levels.