The Gulf of Tonkin Resolution increased the power of the executive branch by-

By giving the president larger powers to use force and other means necessary to face the communist moves in Southeast Asia.

Explanation:

The so-called Gulf of Tonkin Resolution was passed by Congress on August 7, 1964. It authorized president Lyndon B. Johnson "to take all necessary measures to repel any armed attack against the forces of the United States and to prevent further aggression" by the communists of North Vietnam.

It followed the alledged attack on two U. S. Navy destroyers by North Vietnamese boats in international waters of the Gulf of Tonkin. This resolution opened the door to full military engagement by the US in the conflict in Vietnam.