If one moves can he write in his new address on his existing Durable and Health Care Powers of Attorney?

You cannot write on the Durable Power of Attorney.  That will void it.  Similarly, you cannot write on or make any changes to your will by striking through and writing over.  Be sure to let your Attorney-in-Fact know your new address and that is all you need to do.   You may also store a paper listing your new address with your Power of Attorney.  It is permissible to strike through your old address and write your new address on your Health Care Power of Attorney.  Be sure to put your initials right beside the change.  You will need to do this on every copy of the Power that you have filed with doctors and hospitals.