In a large mixing bowl, combine the cooked rice, black beans, corn, salsa, ground cumin, and chili powder. Stir until well mixed.
Spread a thin layer of the rice and bean mixture on the bottom of a 9x13 inch baking dish. Place one tortilla over the mixture, add another layer of the rice and bean mixture, and sprinkle cheese. Repeat until all ingredients are used, finishing with a layer of tortillas topped with cheese.
Preheat oven to 375°F. Cover the baking dish with aluminum foil and bake for 25 minutes. Remove foil and bake for an additional 10-15 minutes until cheese is bubbly and golden brown. Let cool for 5 minutes before slicing.