"exercise the authority" is grammatically correct and usable in written English.
You can use this phrase to mean to give effect to the rights or powers that one has been granted or has been given. For example, "The teacher exercised her authority and reprimanded the student for his inappropriate behavior in front of the whole class."
We need to summon our resources to exercise the authority that allows collective action.
From the start, however, Mr. Duhalde has found it difficult to exercise the authority that normally goes with his office.
The report cited many concerns, but the main one was a failure to meet a basic requirement for successful implementation: having "a single accountable leader" who "has the authority and willingness to exercise the authority to enforce all necessary changes to the business required for successful fielding of the software".
"On the question of whether schools have the ability, or should exercise the authority, to supervise the Internet, globally, the general thought is no, because they are not really in a position to know what is going on at every point in time," he said.
Rather, they claimed to exercise the authority to decide on the exception in the name of the French people, even while they were ruling the French people by the use of dictatorial methods (D 132 47).
The commission had never before exercised the authority it gained in 2011 from the new rule.
Mr. Abbas, who lacked Mr. Arafat's broad popularity, found himself stymied in exercising the authority he had on paper.
But it singles out Lord Martin, who "should have been asking the right questions and... should have taken more responsibility for exercising the authority of his high office".
The reality is that Congress, exercising the authority granted to it under the Constitution, granted the president specific and limited authority to use force against the perpetrators of the Sept. 11 attack.
True, in one sense Mr. Chertoff was simply exercising the authority that Congress had given him, which in the ordinary case is what the separation of powers contemplates from the executive branch.
Therefore, exercising the authority granted by Congress in this legislation, we quickly deployed a $250 billion capital injection program, fully anticipating we would follow that with a program for buying troubled assets.
