Bry Bry - which movements increase punching and kicking power?
benching increases explosive power ..for instance if someone is on top of you, if you are a strong bencher, you could literally just press them off of you..every weight-lifting movement could technically serve some purpose in a fight..training bicep curls wouldnt be worthless either imo as it makes your biceps much strong, increases strength of a choke hold..
It's generally not what you would think of directly (ie, leg extensions to increase kicking power).
Pretty much any Olympic lift is going to train your core and posterior chain which increases your overall strength and applies well to most athletic movements.
As mentioned above, your power in executing striking techniques doesn't necessarily come from big muscles, but ability for those muscles to work together in an efficient way. That's why compound lifts are more valuable than isolated lifts like curls.
You'll also see guys doing lunges or sprints (sometimes with resistance) as this applies well to wrestling and shooting in. Again, it isn't just building muscle on your legs, it's training your body to execute a certain type of motion in a coordinated and explosive fashion.