Power
Tadasana. Vinyasa. Urdhva Hastasana. Yes, these are powerful words, and no, they aren't magic spells straight out of King Arthur. They're Sanskrit words and they're the basis of yogic technique. Learning these words and their deeper meanings is one of the many ways to increase your yoga power.
Each person has their own breath and flow, so it stands to reason each person's method of yoga is individualized. Your power will be to bring everyone to center together, whether you're working with one private client on Wall Street or a dozen Navy Seals. Guidance is something you'll have to learn over the course of your practice. It's kind of the point of even having a teacher; no one wants to pay $100 for a class where the teacher sits back and says, "Do whatever you feel like."
Then there's power yoga. While it certainly has its benefits, it isn't traditional yoga per se. It's an Americanized version of the meditative art that focuses more on the ab-strengthening and calorie-burning properties of yoga than it does on the inner peace and tranquility the ancient monks were reaching for (source).
Wow. Deeper meaning? Peace and tranquility? Isn't yoga just really advanced stretching? That's true—nice call on that one—but that's only part of the overall experience. Now a flexible, calm, spiritual individual like yourself shouldn't be looking for power—unless it's mastery over the negative forces that clutter your mind.
Being able to balance on one foot or bend your left knee over your right shoulder certainly is a powerful ability, but so is just staying perfectly still for an extended moment or two.