Question

Which power does the Constitution give exclusively to the House of Representatives?

Answer 1

The Constitution gives the House the Sole power to Impeach Presidents. 
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Answer 2

The House of Representatives has several powers assigned exclusively to it. The powers are: the power to initiate revenue bills, impeach federal officials and elect the President in case of an electoral college tie.

The House of Representatives is the lower chamber of the United States Congress. It is composed of Representatives that are allocated to each state based on the state's population. The total number of voting representatives is fixed by law at 435.

The presiding officer is the Speaker of the House, the current one is Nancy Pelosi.