Can you change the battery of a power tool to a improved type of battery?

Answer 1

If the improved battery is made to fit into the tool you have then, yes you can. No problem as long as the voltage is the same as your original battery. You may need to buy a new charger though. Some times the new batteries will have special charging characteristics that your old charger may not be able to handle.
Keep in mind that a battery and charger is usually more expensive than buying the new battery and new tool as a kit.
If the new battery doesn't fit in your old power tool then it would be impossible.

Answer 2

If you are referring to the Dewalt batteries for the Dewalt tools the answer is yes