Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel and cube the sweet potato into 1-inch pieces and slice the carrots into half-moons.
In a mixing bowl, toss the sweet potatoes and carrots with half of the olive oil and a pinch of salt and pepper.
In a small bowl, combine the dried rosemary, thyme, garlic powder, salt, and pepper to create an herb rub.
Pat the chicken breast dry with a paper towel, then coat it with the remaining olive oil and the herb rub on both sides.
Arrange the chicken and the vegetable medley on the prepared baking sheet in a single layer.
Roast in the oven for 25 to 30 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are golden and tender.
Remove from the oven and let the chicken rest for 5 minutes before slicing to keep it juicy.
Plate the sliced chicken alongside the roasted root vegetables and serve immediately.