Yes, you can exercise while you are fasting. Should be totally fine if you are in ketosis, and you’ll have plenty of energy. Personally, I have done a large day hike in the mountains while fasting recently, with no problems (I did carry some food, just in case, but didn’t need it). But listen to your body and stop if something doesn’t feel right, or break your fast. In my experience, it is easier to go into ketosis and fast if you had a low-carb diet one to two days before the fast. 72 hours is not that long, so should not be a problem at all for most people.
As long as you hydrate and take electrolytes you will be more than fine. I keep running 5-6 miles daily during long fasts only difference I found loss of sprinting power but on the flip side endurance gets higher. Also another thing, first day you may have lack of focus but your focus and mental clarity comes back 2-3 times more later on.