Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Peel and dice the sweet potato into 1/2-inch cubes and chop the broccoli into bite-sized florets.
Cut the chicken breast into even 1-inch pieces to ensure they cook at the same rate as the vegetables.
In a large mixing bowl, combine the chicken, sweet potato cubes, and broccoli florets.
Drizzle the olive oil over the mixture and sprinkle with garlic powder, onion powder, rosemary, thyme, turmeric, and black pepper.
Toss everything thoroughly until the chicken and vegetables are evenly coated in the oil and spices.
Spread the mixture onto the prepared baking sheet in a single layer, ensuring there is space between the pieces for proper roasting.
Bake for 20 to 25 minutes, or until the chicken is cooked through and the sweet potatoes are tender when pierced with a fork.
Remove from the oven and serve immediately while the herbs are fragrant and the broccoli is slightly crisp.