Your batteries are worn out and need replacing for new fresh ones. They are charging, but not holding the charge. If they are new, they are fakes or worn out.
You can buy batteries which have a higher capacity, more MaH (milli-amp hour) than your current ones.
Having a quick Google, it is a known problem.
try this ... i had the same problem with the same camera and this fixed it.
remove the battery, and remove the memory card ... then re-install the battery & turn on the camera.
this process seems to reset the camera, if the battery ran too low.
now you can re-install the memory card & battery and resume normal operation.
be sure to check for the small flashing green light on the back of the camera (next to the "flash" indicator symbol). it should be blinking when the camera is charging.
i hope this helps you.
nikon coolpix battery exhausted message Google Search