I have a broken stud where the down pipe connects to the rest of the exhaust. The part where there's the two studs/nuts. How do you get it out, it's fucking in there good. I've taken a hammer to it, and it wont budge.

Any suggestions?

If enough of the stud is sticking out you can use channel locks or vice grips to twist out. If not, going to have to use reversible drill bit or extractor.