What term refers to the role of the president as the head of all of the branches of the military.

Commander in chief.

Explanation:

The President of the United States of America is the Commander in Chief of all the branches of military of the United States, according to the clause 1 of article 2, section 2 of the constitution of the U.S.

The President, being the Commander in chief of all forces, has the full authority to give commands to all the military generals and to decide the use of the troops, weapons, ships, etc.

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