Power doesn't affect stall speed. The airplane always stalls when it exceeds the critical angle of attack. You can exceed this at any power setting. Maybe you're confusing slow flight. " Any airspeed at which an increase in angle of attack, load factor or reduction in power will induce an immediate stall." When flying in slow flight, if you maintain constant back pressure and suddenly reduce power, you stall. Not directly because of power, but because with the reduction in power, the angle of attack will slightly increase with constant back pressure, thus exceeding CLMAX.
Slow flight and power also deal with the region of reversed command. Where you are on the backside of the power/drag curve and more power is required to go slower. This merely has to do with so much induced drag due to the high angle of attack that in order for the airplane to operate at such a slow airspeed and high angle of attack, you need more power.
To demonstrate that power doesn't affect stalling
speed, take a 172 to up to about 4,000AGL, set the power to idle. Just pitch up until it stalls (power off stall). Let it recover then do a power off steep turn at 60' bank while trying to maintain altitude, you will accelerate the stall and probably stall somewhere in the ball park of 60kts. You can also initiate a descent at about 500'FPM power off, and abruptly pitch up (without exceeding airframe limitations) and you'll see an accelerated stall. Of course do this with an instructor.