Preheat your oven to 400°F and line a baking sheet with parchment paper. Trim the woody ends off the asparagus and slice the carrots into pieces that are similar in size to the asparagus.
Arrange the asparagus and carrots on the baking sheet. Drizzle them with olive oil and season with garlic powder, onion powder, cayenne pepper, salt, and freshly ground black pepper.
Spread the vegetables in a single layer and roast them in the preheated oven for 20 to 25 minutes, stirring halfway through, until they are tender and lightly browned.