I purchased a GE Z735 digital camera that turns off

If you've recently dropped the camera you may have damaged the lens tube (housing) or jarred the zoom mechanism off of its track. Both problems will cause the camera to shut off in order to prevent further damage, and both require professional repair. If the camera has not been dropped, your problem may be due to weak/worn out batteries or corrosion on the battery contacts inside the camera which can prevent the full power of the batteries from flowing into the camera. Try this free fix before you do anything else: remove the batteries and wipe the camera contacts firmly with a dry cloth (heavy corrosion may require cleaning with a wire brush, steel wool, or sandpaper). Remove any residue that may have fallen into the battery compartment during cleaning, then wipe both ends of the batteries and place them back in the camera. This cleaning clears the problem about 90% of the time. If it doesn't work for you, your batteries may be too weak/worn to properly power the camera, or the camera may require professional repair.