It depends a lot on many things. Your question is so broad that it is difficult to make a proper answer, but I'll try.
About 3betting, it depends on what the positions are. If you are MP vs UTG you probably don't have to 3bet AK hands. But in late positions where ranges are wider, it makes sense to 3bet with a wider range and AK is definitely one of your best hands. On top of your equity vs villains calling range you should also think about how often you make villain fold immediately with your 3bet. And also you should consider the times where villain just calls your 3bet and you get to play postflop. If you are not all-in preflop, the equities don't mean much.
It is the same thing with 4betting. There will be many 3bet bluffs in certain spots and you have to defend against those. AK still is one of your best hands and when you think about how often villain just folds directly, you start to see how profitable the spot is.
Against 5bet shoves you don't need to win 50% of the time to make profit. You have already invested so much money. If you have 4bet your AK to 25bb and villain shoves (total 100bb).. Then the pot will be 125bb total and you have to call just 75bb more. This means that you start to see profit on the long run even if you win only 38% of the time.
These things depend a lot on positions, stack depth, action preflop and so on, so I can't give you an answer how to play AK on every situation. But I hope you got the point. It is not as simple as just looking at the equities