Final answer:
The power to settle the dispute between New Hampshire and New York regarding Vermont lies with the Supreme Court.
Step-by-step explanation:
The power to settle disputes between New Hampshire and New York regarding Vermont lies with the judicial branch of the federal government, specifically the Supreme Court. The Supreme Court has the authority to interpret and apply the laws of the United States, including resolving conflicts between states. It has the final say in determining the boundaries and jurisdiction of states.
In the case of the disputed area between New Hampshire and New York regarding Vermont, the settlement in favor of New Hampshire in 1741 established its sovereignty over the region. Any future disputes or conflicts regarding this matter would likely be resolved through a legal process that could potentially reach the Supreme Court.