We didn't figure it out, we made it up.

Brackets being first makes sense because all that brackets do is change the order. If they weren't first they'd be useless.

The others are fairly arbitrary but do make some sort of sense. Exponents are repeated multiplication, multiplication is repeated addition. So it does make sense to go from the "most powerful" operation to the least powerful.

But if we wanted to we could have an order of operations that does addition first and exponents last. We'd just have to rewrite all our equations if we wanted to get the same result.