1. **State the problem:** Find the exterior angle sum of a polygon with 500 sides (a 500-gon). 2. **Formula and rule:** The sum of the exterior angles of any polygon, regardless of the number of sides, is always $$360^\circ$$. 3. **Explanation:** This is because the exterior angles, one at each vertex, always add up to a full circle around the polygon. 4. **Apply the formula:** Since the polygon has 500 sides, the sum of its exterior angles is still $$360^\circ$$. 5. **Final answer:** The exterior angle sum of a 500-gon is $$360^\circ$$.