Final answer:
The Supreme Court's primary responsibility is to establish legal precedents that will guide the lower courts' decisions.
Step-by-step explanation:
The Supreme Court's primary responsibility with regard to the lower courts is to establish legal precedents that will guide their decisions. The Supreme Court's decisions are binding on the lower courts and set the standards of interpretation that they must follow. By interpreting and applying the Constitution, the Supreme Court ensures consistency and legitimacy in the judicial system.