# Show that $P^A \neq EXP^A$ for all oracles A

I knew that $$P \neq EXP$$ by Time Hierarchy Theorem. But, I'd like to show that $$P^A \neq EXP^A$$ for all oracles A. How can I do it?

I knew that If I make A=EXP, PSPACE, NP, and many others, then this would show that the inequality holds. But, how can I prove it for all oracles? Can you give me hints?

Notes: I don't think that there exists some oracle that $$P^B = EXP^B$$ for some oracles B since it seems to me that $$P \neq EXP$$ using THT relativizes. But I don't know why it relativizes? Consider this as a minor question of the above question.