Rama ultimately convinces Parashurama of his divine nature through a demonstration of his extraordinary prowess and divine attributes. In the epic Ramayana, after Rama breaks the bow of Shiva during Sita's swayamvara, Parashurama, a fierce and powerful sage known for his own formidable strength and a devotee of Shiva, arrives in anger to challenge Rama.
Parashurama initially doubts Rama's abilities and questions his identity. To prove his divine nature, Rama accepts Parashurama's challenge and demonstrates his exceptional skills and divine powers. He takes up the bow of Vishnu, which Parashurama carries, and effortlessly strings it, showcasing his unmatched strength and divine lineage as an incarnation of Vishnu.
This act of effortlessly handling the bow, which only a divine being could do, convinces Parashurama of Rama's true identity as an avatar of Vishnu. Realizing that Rama is indeed the divine incarnation, Parashurama acknowledges his own mistake, pays his respects, and withdraws peacefully, recognizing Rama's supreme nature and his role in the cosmic order.