Final answer:
The President appoints the leaders of the judiciary branch with the Senate's approval, as determined by the Great Compromise and practices like the Judiciary Act of 1789.
Step-by-step explanation:
During the Great Compromise, it was determined that the leaders of the judiciary branch would be appointed by the President with the approval of the Senate. This was a solution that provided a balance between the Federalist's desire for a strong centralized government and the Anti-Federalist's insistence on states' rights. For example, in the Judiciary Act of 1789, which established the federal judiciary, judges of the lower courts were appointed following this method, as were the Supreme Court justices. This process is intended to ensure an independent judiciary, capable of upholding the law without undue influence from changing political climates.