Preheat the oven to 400°F. Line a large baking sheet with parchment paper.
In a mixing bowl, combine the diced chicken, olive oil, chili powder, cumin, garlic powder, onion powder, salt, and black pepper. Toss until the chicken is evenly coated.
Spread the seasoned chicken evenly on the prepared baking sheet. Bake for 15-20 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F.
While the chicken is baking, warm the corn tortillas in a dry skillet over medium heat for about 30 seconds on each side until pliable.
Once the chicken is done, remove it from the oven and assemble the tostadas. Spread a layer of refried beans on each tortilla, top with the baked chicken, and sprinkle with shredded cheese.
Return the assembled tostadas to the oven and bake for an additional 5-7 minutes, or until the cheese is melted and bubbly.
Remove from the oven and top with diced tomatoes, black olives, cilantro, and avocado. Serve with sour cream if desired.