1 What is the author's main argument for distributing powers among largely independent branches of government?

In James Madison’s Federalist 51.

The author's main argument for distributing powers among largely independent branches of government is:

to balance any one person or branch whose ambition is overwhelming, thereby controlling the abuses of government.  

Without separation of governmental powers as advocated by James Madison, anarchy will be reigning throughout the United States.

Explanation:

The Federalist No. 51 was written by James Madison as an essay.  It was originally published on February 8, 1788.  In this essay, Madison recognized the need for the separate and distinct exercise of the different powers of government so that liberty was not put in peril, with chaos taking over as witnessed recently in the last days of the Trump administration.