Preheat your oven to 400°F and line a large sheet pan with parchment paper for easy cleanup.
Peel the sweet potato and cut it into 1/2-inch cubes, and slice the carrots into thin rounds.
In a bowl, toss the sweet potatoes and carrots with half of the olive oil and a pinch of the rosemary and thyme.
Spread the potatoes and carrots onto the baking sheet and roast for 10 minutes.
While the vegetables are roasting, rub the chicken breast with the remaining olive oil, rosemary, thyme, garlic powder, onion powder, and black pepper.
Remove the pan from the oven, move the vegetables to one side, and place the chicken breast and broccoli florets on the other side.
Return the pan to the oven and roast for another 15 to 20 minutes until the chicken reaches an internal temperature of 165°F.
Remove from the oven and drizzle the fresh lemon juice over the chicken and roasted vegetables before serving hot.