Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Peel the sweet potato and cut it into 1/2-inch cubes, then chop the broccoli into bite-sized florets.
Pat the chicken breast completely dry with a paper towel to ensure the spices stick and the meat roasts properly.
In a large mixing bowl, toss the sweet potato cubes and broccoli florets with 0.5 tablespoons of olive oil, half the salt, and half the pepper.
Rub the chicken breast with the remaining 0.25 tablespoons of olive oil, garlic powder, smoked paprika, and the remaining salt and pepper.
Arrange the chicken and sweet potatoes on the prepared baking sheet in a single layer, leaving space for the broccoli later.
Roast for 10 minutes, then remove the pan briefly to add the broccoli florets to the sheet.
Return the pan to the oven and roast for an additional 12 to 15 minutes, or until the chicken reaches an internal temperature of 165°F.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure it stays juicy.