Nope, definitely a big No. It's absolutely not safe to leave your precious cryptos on an exchange. For one, they store your private key on an online server, so you can imagine how 'safe' that is. Secondly, if that exchange gets hacked (which let me tell you happens a lot. Take the recent Binance hack for an example).
What you can do is have a proper wallet. Online wallets aren't that safe either, but some of them are trust-worthy. The best would be to have a hardware wallet. That way you'll never have to worry about your crypto again.