Preheat oven to 350 F. In a small bowl, whisk together olive oil, garlic powder, pepper, and salt. In a medium bowl, toss together the brussels sprouts and nuts with the olive oil mixture. Place the mixture onto a baking sheet, and bake for approximately 20-30 minutes, tossing occasionally throughout the cooking process. When brussels and nuts have reached desired crispiness, remove from oven and place into serving bowl. Toss with pomegranates and serve immediately.