Final answer:
The old man convinces Santiago of his power by showing hidden knowledge.
Step-by-step explanation:
The old man convinces Santiago of his power by showing hidden knowledge. This is seen when the old man accurately describes Santiago's dream about a treasure in the Pyramids of Egypt, a dream that Santiago had not shared with anyone.
By revealing this hidden information, the old man proves his ability to tap into a higher power or source of knowledge. This convinces Santiago that the old man possesses a special power or wisdom.