what is the most powerful branch of government?
All three branches of government in the U.S.A., the Executive, Legislative and Judicial, were made to be equal. One branch does not over power the other. This was one of the main concerns of the Founding Fathers when they were creating the Constitution. This is why the systems of checks and balances, and the separation of powers (idea originally by Montesquieu) are used. The three branches and their powers can be found in the first three articles of the Constitution. The people give the power to the government, as it says "We the People," in the Preamble to the Constitution, and this power is divided to keep balance between order and liberty. All branches are equally important and serve different purposes.
A good book and easy read that would help you to understand the branches more in detail is The U.S. Constitution for Everyone by Jerome Agel and Mort Gerberg, a Perigee Book.
Without question, it is the Legislative branch, that is, Congress.
Congress passes the laws, the annual budget of the United States, must approve (confirm) Federal Judgeships and U.S. Attorney's, etc.
They have power to add or remove by any # the Supreme Court Justices (one time there were 11 members), and inferior federal courts.
Although Washington, D.C. is under HOME RULE (about 1971), Congress still maintains certain oversee powers of the federal district, as we note the DC stands for District of Columbia, as the City of Washington is co-extensive with the federal district.
The executive (federal) branch.