If you don't already know this, a powerband is not an actual object.
It refers to the rpm range where an engine makes it's most power. This may or may not be a "useable" range, like in the case of the R6 (dyno below), unfortunately the US is a numbers game so peak horsepower is marketed more than anything else.
If you are riding an R6 at 3,000 rpms, you will be bogging it.
You then go Wide open throttle (WOT) the revs will climb slowly until you reach 5-6,000 and the bike will start to pull harder. as the revs climb, approaching the powerband the bike will continue to accelerate harder and harder and when you reach the very high RPMs it will pull very quickly into the over-rev range. It is still making a lot of horsepower, but at this point (15,500 rpms) the bike definitely stopped accelerating as hard and it's time to change gears.
If then engine is spinning between 10-14k it is going to be very responsive, have the most overall horsepower and accelerate the hardest.
Hopefully this clears things up a little bit