Light Yagami ensures his continued dominance and influence over the Death Note's power by meticulously planning his actions, manipulating others to do his bidding, and constantly staying steps ahead of his adversaries. He also strategically uses the Death Note to eliminate those who pose a threat to his plans, further solidifying his control over the situation. Additionally, he maintains a calculated and cold demeanor to instill fear and respect in those around him, ensuring they do not challenge his authority.