The BEST best strength training exercise
Better for strength and power...
Better for stability...
Better for carryover to functional outside-of-the-gym performance...
Better for safety...
And you're probably not doing it.
The exercise is split squats! They seriously deliver the good.
They are awfully difficult and tiring. By the time you can split squat 6 to 10 reps one each leg, with your body weight on the barbell (or holding dumbbells), you're talking 12 to 20 reps of intense total body strength, balance, and stability effort. One feels like an eternity.
Strength and Size with less risk
Split squats are an exercise that allows you to load up some serious poundage, which is needed for building strength and size. While step-ups and -pure- single leg balancing work (aka single leg box squats, bowler squats, etc) are often worthwhile, they do not allow you to handle heavy loads. But split squats allow sufficient loading to strap some mass to the thighs and hips.
On the other hand, split squats demand less absolute load than conventional squats or deadlifts, thus saving some of the extreme compressive loads on the spine and knees. Along those lines, since proper form in split squats allows for a more upright torso, they demand much less front-to-back shear on the spine as compared to conventional squats and deads.
Also in terms of safety, split squats just don't hold the same ego factor as other traditional strength training movements. You won't see internet heroes bragging about how much they can split squat, and you won't see young men loading up more than they can handle simply for showmanship in the weight room.
Balance and stability in three planes
I stated above that split squats place less sagittal plane stress on the spine. That's good, since plenty of other resistance exercises do and we often have too much of that to begin with. But split squats are unique in that they demand a lot of stability in the other two planes of motion.
Split squats make extreme demands on total body balance and stability. Power cleans, squats and deads are performed on two legs and occur primarily in the sagittal (front to back) plane of motion. But most athletic and everyday life endeavors take place while a person is NOT perfectly squared up on two legs or has one leg on the ground (as in running and hurdle type leaps and bounds). The forces of everyday life occur across all three planes of motion (including rotational and side-to-side).
Even well trained athletes struggle with split squats when they begin. The evidence of strength, balance, and stability demands shows up as they lose their balance, their torso twists, and hips sway to the side. I hope it goes without saying, that one should start light and progress slowly as they become capable of maintaining form and not spilling over!
How to split squat
Most people should begin with holding a relatively light resistance such as a 5 to 30- pound medicine ball, kettlebell, or dumbbell, in front of their chest. Place a bench or box approximately two or three feet behind you and drape the top of one foot over it. Now, with 80 to 90% of your body weight on the front leg, and the back leg being used for balance, squat down by bending the lead knee and hip. The torso should not drift toward the back foot. But you also don't want the lead knee going out over in front of the lead foot. Also, pushing too hard with the back/balance foot will sooner or later cause knee irritation. Keep the load on the front heel.
Struggle, master the form, up the resistance. Using a barbell on the shoulder rather than resistance front loaded at the chest creates even more challenge to the core and balance. I usually recommend one warm up then three "work" sets of 6 to 10 reps on each leg. It's well worth it.