What's the best way(s) to improve your punching power?

Yes

 

How exactly did you come to that conclusion? I like your muscle naming scheme btw :smoke

 

the 'big back muscle'??

 

It's right between the "somewhat smaller back muscle" and the "funny looking medium sized side muscle"

 

Practice makes perfect. Hit the bags a lot, and then hit them again until you can't hit them anymore. Power comes from the whole body as one unit along with muscle memory and technique, a proper punch thrown correctly is the most powerful.