Final answer:
The exclusive power of the House of Representatives is the sole power of impeachment. This power permits them to initiate charges against federal officials for serious crimes. They also elect their own Speaker and fill vacancies through special elections.
Step-by-step explanation:
An exclusive power of the House of Representatives is the sole power of impeachment. This unique function allows the House to charge a president, vice president, or other civil officers of the United States with crimes such as 'Treason, Bribery, or other high Crimes and Misdemeanors.' The actual impeachment proceedings begin in the House, where they hold the sole authority to impeach, but any subsequent trial is conducted in the Senate.
The House also has the prerogative to choose their Speaker and other officers without interference from the Senate or any other branch of government. The Speaker acts as the leader of the House and can take over the presidency if both the President and the Vice President are unable to serve.
Additionally, Article I, Section 2 of the Constitution tasks the House with choosing its own leadership and outlines the process for filling vacancies. When a member of the House resigns or passes away, it's the responsibility of the governor of that representative's state to call for a special election to fill the vacancy.