In theory, yes, your output hp is constant regardless of your gearing system. HP is a function of torque and rpm. At constant hp, a decrease in rpm is followed by an increase in torque, linearly. This is the way a physicist would analyze it. But because this is real life and not theory, we need to analyze it from an engineer point of view.

You'll have parasitic drag in a real system. And the more gears you go through the more drag you have, and therefore more hp converted to hp.

Theoretically, you should dyno the same hp numbers in any gear, but you don't. You get the least hp from reverse because it goes through an extra set of gears. You also get more drag with two gears of different ratio (therefore radius and contact points, assuming constant pitch) than you do with two equal radius gears.

Assuming that you do not need to go through a set of gears in high range :



Then high range would have less parasitic drag loss than low gear.

Extreme offroaders who uses a second gear reduction system to further lower the output ratio will experience an even greater power loss. Same goes for geared poral axel systems. In theory hp is constant no matter how you gear a system. But in reality gears cost power.