Turn camera over, looking at the bottom straight at the tripod socket, with the battery compartment to the left. Bring you eye up from the tripod socket to the lens mount without moving the camera. About a 1/3 ofthe way down from the silver mounting ring you'll see black numbers on the black surface of the raised portion of the camera body.
George... I can't help you with the MB-15 battery pack, but you might also have a look at the Nikon website. There are some forums there, and in fact, I found a thread that showed where the serial number is on a lot of their products... it just didn't include any of their film cameras....grrrr... but you might do a search in those forums if there's no answer here!