I'm not entirely sure here but am in the process of changing from a standard to a power this year.
That "rubber" thing, as you put it, is a bushing that reduces stress on the fiberglass from the antenna vibration and torquing with the wind. Mine was "frozen" into the body ( and rock solid) and took some convincing to get out without doing any body damage, unfortunatly, cracked the mount hole. It goes all the way from top to bottom through the body. I got mine out by forcing the antenna through the body mount hole from top to bottom while someone pulled the mount from underneath, once the antenna was out I could compress the bushing, or at least that's what I thought!!!!! That's how I cracked the mount hole, so be careful.
Hope that helps.