Question: does the supreme court have the power to declare a law unconstitutional

Answer: Yes, Two landmark decisions by the U.S. Supreme Court served to confirm the inferred constitutional authority for judicial review in the United States: In 1796, Hylton v. United States was the first case decided by the Supreme Court involving a direct challenge to the constitutionality of an act of Congress, the Carriage Act of 1794 which imposed a ``carriage tax''. The Court engaged in the process of judicial review by examining the plaintiff's claim that the carriage tax was unconstitutional. After review, the Supreme Court decided the Carriage Act was constitutional. In 1803, Marbury v. Madison was the first Supreme Court case where the Court asserted its authority for judicial review to strike down a law as unconstitutional. At the end of his opinion in this decision, Chief Justice John Marshall maintained that the Supreme Court's responsibility to overturn unconstitutional legislation was a necessary consequence of their sworn oath of office to uphold the Constitution as instructed in Article Six of the Constitution.