You can't power attack if your Strength is less than 13.
Let's see how much we can anti-power game without relying on magic.
Urgthk, a 20th level human ranger, has been having a bad day. He has been poisoned by a giant wasp, then rendered weaponless by his greatest enemy, the FearMeister. Urgthk managed to escape into the sewers, procuring as weapons an incredibly small whip he stole from a baby pixie, and a kama sized for an ogre. He also stole some armor, but unfortunately it's half-plate, and he's not proficient with it. He's trying to escape some rats in the sewer, so he's shimmying through a 3-ft. wide pipe when the FearMeister appears at the end of the pipe just feet from Urgthk's face, spouting off intimidating insults, then tossing flash powder and a tanglefoot bag at Urgthk.
We have a 20th level ranger (+20 BAB) with Str 13, Int 13, and Dex 1 (poisoned), Power Attack, Combat Expertise, Improved Combat Expertise, and Weapon Finesse (-5 penalty with Dexterity), wearing armor he's not proficient with (-7), fighting with two weapons (-6/-10, since he treats the whip as his primary weapon, and the kama as off-handed, and he can't make use of his two-weapon fighting feat while in heavy armor) while prone (-4), dazzled (-1), entangled (-2), shaken (-2), and squeezing through a space (-4). Figuring he'll not hit anyway, he power attacks for 20 (-20), uses Improved Combat Expertise for 20 (-20), and fights defensively (-4).
Because the whip sized for a fine creature (-8 penalty for size difference, -4 for non-proficiency), and the kama is sized for a Large creature (-2 penalty for size, -4 for non-proficiency), Urgthk's attack bonus is:
Kukri - +20 +1 -7 -10 -4 -1 -2 -2 -4 -20 -20 -4 -2 -4, for -59/-64/-69.
Whip - +20 -5 -7 -6 -4 -1 -2 -2 -4 -20 -20 -4 -8 -4, for -71/-76/-81/-86.
Because he's denied his Dexterity bonus to AC, he does not benefit from the dodge bonus to AC.
Beat that.