Are you sure that is the correct information? I know that some CEX (like YoBit) had a fixed withdrawal fee that was quite high even when they had some reputation, but if someone asks for even $200 to withdraw your BTC to a non-custodial wallet, then it's not a fee, it's pure robbery.
I don't have account on Poloniex and can't check that by myelf, but Pmalek should be right.
See
the post made by Oshosondy on another thread some days ago.