Final answer:
The exclusive power held by the House of Representatives is the sole power of impeachment against the President, Vice President, and other federal officials for serious misconduct. Additionally, the House has the authority to control the government spending by introducing revenue bills and has unique roles such as choosing their Speaker.
Step-by-step explanation:
The House of Representatives alone holds several powers not shared with other branches of the federal government. One of the most significant is the sole power of impeachment. This means that the House has the exclusive authority to charge the President, Vice President, or other federal officials with 'Treason, Bribery, or other high Crimes and Misdemeanors.' The House acts as the prosecutor in any impeachment proceeding, and if an official is impeached, a trial is then conducted in the U.S. Senate, which can lead to the individual being removed from office.
In addition to the power of impeachment, the House has exclusive privileges such as selecting their Speaker and other officers. Furthermore, the House is vested with the 'power of the purse,' which entails controlling government spending. Only the House can introduce revenue bills, reflecting the importance of the House's role in federal fiscal policy. These powers serve as checks and balances on the executive and the judiciary, ensuring a separation of powers and preventing abuse of authority within the government.