How does the Constitution support the idea of the rule of law in the executive branch?

Rule of Law is a principle that means that everyone is answerable to the law. Nobody is exempted.

The Executive branch of the government is in charge of implementing the law. Thus, they are tasked to ensure that everyone must follow the law regardless of their position in life or in the government.

The government and its officials and agents together with individuals and private entities are all accountable to the law. Thus, the rule of law applies to everybody.