'extraordinary authority' is correct and usable in written English.
You can use it to describe someone or something with a large amount of power posed over others. For example, "The head of the United Nations has extraordinary authority when it comes to resolving international disputes."
"We are giving the president extraordinary authority," he said on the Senate floor.
Here, though the impression has been spread over two days of extraordinary authority with one characteristic becoming increasingly apparent.
It didn't hurt that Vadim Repin was there to play the Brahms Violin Concerto with such extraordinary authority.
Once he began to review for the New Republic and then the New Yorker, his opinions gathered an extraordinary authority.
In addition to the sheer physical skill that she exhibits in this scene — and throughout the play — she uses her voice with extraordinary authority.
Thanks to the disastrous "monarchical principle" kept alive by the long-serving chancellor, the arch-conservative Otto von Bismarck, the young Kaiser had extraordinary authority.
"I would rather not be in the position of asking for extraordinary authorities to support" Fannie and Freddie, Mr. Paulson said during a speech at the New York Public Library.
"When the Congress provided the extraordinary authorities in response to the Al Qaeda attacks of Sept. 11, 2001, it expected that tax dollars would be managed carefully so as to provide assistance to the victims of the attack, to secure our homeland and to improve our national security," the lawmakers said in a letter to the White House.
He began to put immense pressure on the media, intellectuals, nonprofits, businesses and opposition, and he empowered the security forces with extraordinary authorities.
These gave extraordinary range, authority and depth to all his writing.
The petition gave birth to the Mexican environmental movement, endowing it with extraordinary moral authority.
