Light Yagami ensures his continued dominance and influence over the Death Note's power by meticulously planning each move, maintaining a high level of secrecy about his actions, manipulating those around him to serve his agenda, and constantly adapting his strategies to outwit his opponents. Additionally, he uses his intelligence, charisma, and strong sense of righteousness to gain support and loyalty from others, allowing him to solidify his control over the Death Note's power.