Preheat oven to 425°F (218°C).
In a large bowl, toss the potatoes, sweet potato, onion, carrot, and garlic with 2 tbsp olive oil, ½ tsp salt, and ¼ tsp black pepper. Spread them out in a single layer on the baking sheet.
Pat the chicken dry with paper towels (this helps crisp the skin). Rub the remaining 1 tbsp olive oil over the chicken. Season with the remaining salt, pepper, garlic powder, onion powder, paprika, and thyme/rosemary.
Place the chicken pieces skin-side up on top of the vegetables. This allows the juices from the chicken to drip down and flavor the veggies.
Roast uncovered for about 40-50 minutes, or until the chicken skin is crispy and golden brown, and a thermometer inserted into the thickest part reads 175-180°F (80-82°C).
If you want even crispier skin, broil on high for 2-3 minutes at the end.
Let the chicken rest for 5 minutes before serving.