Bring a very tall ladder into the room with the smoke detector on the vaulted ceiling. If the smoke detector is near the wall, use a long lean-to ladder like many people use on the outside of their homes. If the smoke detector is not near any walls, you will need a 12-foot or 16-foot "A-frame" ladder. If you don't own a ladder, rent one from a tool rental shop or home improvement store.
Put the batteries in an easy-to-reach pocket, pouch or tool belt. Climb the ladder until you can easily reach the detector, but do not climb up onto the top step.
Open the smoke detector by looking for and then pulling the tab. Be very careful at this height. After the detector is opened, remove the old batteries, paying attention to the direction the positive and negative poles are facing.
Put the new batteries in the smoke detector. Close the smoke detector until it snaps. Push the button on the detector to test that the batteries were installed correctly.