understanding how exchanges "store" bitcoins
You access the bitcoins in your account at an  exchange through their web interface only. They keep the private keys to those those bitcoin addresses hosted at their exchange. So, even though its your account, they control the private keys. 
If you want to move those funds outside the exchange, pay them to yourself on a wallet hosted on a device you control. An exchange is unlikely to give you access to the private keys, because then the private key would be out of their control and they could not guarantee that the funds were safe nor be held responsible if they were spent.