Suppose you work at Acme doing your usual: fooing the bars. Now you are promoted and this means you have a new competency: you will be bazing the quxes as well. Therefore you have the new responsibility that all quxes are bazed in due time and you are supposed to propose new quxes as well. To make sure you can perform your new duties, you are given new powers: you may prioritize the quxes to baz as you see fit, and also you may assign some quxes to your colleagues.
Did I use the the words competency, responsibility and powers correctly?