Final answer:
The Supreme Court established the power to overturn unconstitutional government acts in the case of Marbury v. Madison in 1803, which laid the foundation for the principle of judicial review.
Step-by-step explanation:
The Supreme Court first declared that the courts have the power to overturn government acts that conflict with the Constitution in the case of Marbury v. Madison in 1803. This case established the principle of judicial review, which became a cornerstone of the United States legal system.
Chief Justice John Marshall delivered the decision, stating that an act of the legislature that is repugnant to the Constitution is void. The significance of this is profound, as it ensures that no law or governmental action can supersede the ultimate authority of the Constitution.