There is no real difference. You can use either one, although it is true what Zac says: ''exactly' is more common in everyday speech

Precisely emphasise measurements and time, like 2mm precisely, 2 o'clock precisely. Exactly usually use in oral language, more like confirmation of your opinion, ex. That's exactly what I said!

Although there's no real difference, I think that there are certain contexts in which one word is better than the other. So you can't simply substitute. For example you are more likely to hear someone say: "I'm a precise person" rather than "I'm an exact person", or "I precisely asked about xyz", rather than "I exactly asked about xyz". Keep practicing with them and you'll overtime you'll gain a sense of when to use each one.

I agree with Gary that these words are the same, and there is no difference in the meaning or use.