How you use your breath will affect how you use your body
And vice versa of course
But let's stay with this for a second.
If you want to demonstrate high levels of strength, tension, stability then you will want to take a big inhale and keep as much of that air in as possible.
If you want to demonstrate maximal explosive power, and sudden burst of strength and stability, you will want to take a good breath in and blast it out as fast as possible
If you want to demonstrate endurance and stamina, you will want to breathe in a cyclical manner, in a close rhythm with the movement.
If you want to demonstrate mobility or flexibility, you will want to breathe easy, exhaling in a long slow manner.
Our inhale can be correlated to high arousal, our sympathetic nervous system. This is action, it's go, its power.
Our exhale can be correlated to low levels of arousal, our parasympathetic nervous system. This is rest, relax, chill.
So consider the exercise or activity you are doing, and you'll work out the breath pattern that will be commensurate with that performance.