The phrase "a legitimate exercise of" is correct and usable in written English.
It can be used when discussing the validity or appropriateness of an action or authority, often in legal or formal contexts.
Example: "The court ruled that the new regulations were a legitimate exercise of the government's power to protect public health."
Alternatives: "a valid use of" or "an appropriate application of".
"It was legitimately passed, and a legitimate exercise of the power of the Legislature and the governor, and I will defend it".
a legitimate exercise of the taxing power.
DACA is a legitimate exercise of that presidential power.
(The court nevertheless upheld the individual mandate as a legitimate exercise of Congress's taxing power).
In a detailed opinion, the Court of Chancery upheld the Rights Plan as a legitimate exercise of business judgment by Household.
American courts have long construed this to mean that some showing of "publicness" is a condition precedent to a legitimate exercise of the power of eminent domain.
Much of the criticism on this score strikes me as redundant; getting more women into the boardroom is a legitimate exercise, besides which, many of the lessons from Lean In are translatable, particularly those on negotiating.
In truth, because a state legislature's power in this matter is plenary, it would be an entirely legitimate exercise of its authority to drop out of the compact anytime before the deadline for selecting electors — be it July 21 of an election year or Nov. 9.
But free speech will be defeated if we come to believe that the "heckler's veto"—through which too many speakers have been shut down on campuses of late is itself an equally legitimate exercise of free speech.
George Will has written that, "A defining attribute of a government is that it has a monopoly on the legitimate exercise of violence.
The idea is to convince federal courts that the proposed ban is more than a manifestation of a prejudice against Islam masquerading as the legitimate exercise of the executive branch's responsibility to promote national security.
