Okay, let's make it slow for you.
"As for Buggy the bombastic clown considering his formidable pedigree and the fact he got these two to yield to his authority, we have given him a bounty of..."
Nothing about power. It's about authority. The marine thinks buggy has the authority to say "Hey Mihawk, Strongest Swordsman on the World, go and fuck up Kizaru" and they are certain Mihawk will go and fuck up Kizaru. That's why buggy's bounty so high.
What do you not get here bro? How can someone's eyes be so agenda-clouded?