I teach basketball to high school kids and want to keep increasing their power output. However, the boys don't have access to heavy weights but to have access to bands and lighter (20lb) dumbbells. Is there a way to gain more power with only the resources?
You need to go to the basic of what in fact is "power" to understand on how to properly develop it.
The best example would be using physics definition of mechanical power:
Power = Force * velocity
The part You want to maximize is the balance between two variables in that equation. Please note that there is a tradeoff between Force and velocity. I would say You should provide a stimulus of perceived maximum velocity at any given available Force. This will be different for each muscle You want to target.
I would say that it is totally possible to practice with the means that you have. Even throwing the dumbbells' forward from squatting position initiating a short 2 step run should be sufficient. This is sometimes done in track and field training.
Jump squats with a dumbbell in each hand seem to be a good option. Twenty pounds is light for dumbbell swings but they'd still provide some fast-twitch stimulus for the glutes and hamstrings. Don't forget sprints and unweighted jumping & hopping drills, too.
Strength work would provide a good foundation to the explosive efforts, so lunges, rear-leg-elevated split squats, and other single-leg work with the dumbbells would be useful.
Get your players access to real weights, such as barbells, and have them to do the squat, deadlift, overhead press, bench, and power clean. Otherwise, after a week of training teenage boys who are full of testosterone and HGH, they will have adapted to everything rubber bands and 20 pound dumbbells can be done with.
20 pound dumbbells and bands won’t make you very strong or very powerful. If they did, that’s what the World’s Strongest Man competitors would train with. Olympic Lifting would be about demonstrating your ability to stand one legged on a trampoline while twirling dumbbells like a baton. Complexity does not equal better training.
Also, if these kids aren’t in Tanner Stage 4 yet, they’re not ready to train. You’ll just wonder why nothing is happening.