Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel the sweet potato and cut it into 1-inch cubes.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, rosemary, garlic powder, salt, and pepper.
Place the sweet potato cubes on one side of the baking sheet and drizzle with half of the lemon-herb oil mixture, tossing to coat evenly.
Roast the sweet potatoes for 10 minutes.
While the potatoes roast, brush the remaining lemon-herb oil mixture onto the chicken breast.
Remove the baking sheet from the oven and place the chicken breast and broccoli florets on the empty side.
Return the sheet to the oven and roast for an additional 18-22 minutes, or until the chicken reaches an internal temperature of 165°F and the potatoes are fork-tender.
Let the chicken rest for 5 minutes before slicing and serving alongside the roasted vegetables.