The phrase "exert the most influence" can be substituted with several synonyms to convey a similar message. One could use words such as "dominate," "govern," or "control" to imply a high level of authority or impact. Other options include "dictate," "persuade," "sway," or "manipulate," which suggest the ability to direct or change someone's behavior or opinions. Additionally, "command," "instruct," or "guide" can indicate a strong leading role. Choosing the appropriate synonym depends on the context and desired tone of the message. Nevertheless, all of these words imply an assertive and influential communication style.