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The phrase "has a vast influence" is correct and can be used in written English.
It is typically used to describe something or someone that has a significant impact or control over a situation or group of people. Example: "The media has a vast influence over public opinion." This sentence means that the media has a strong ability to shape the way people think and make decisions through the information and messages they present.
Exact(1)
These and the current data indicate that the role of serum in cancer cell migration and invasion is more than just a chemoattractant and that growth factor signaling has a vast influence on the effects of hypoxia in migration and invasion assays.
Similar(59)
Coover's often avant-garde work was far from commercially successful, but he had a vast influence on a generation of postmodern writers, including David Foster Wallace, Dave Eggers, and Rick Moody.
Although many of his studies are small and often financed by drug makers, Dr. Biederman has had a vast influence on the field largely because of his position at one of the most prestigious medical institutions.
Meal for two £150 Fergus Henderson's Clerkenwell temple to nose-to-tail eating, St John, has had a vast influence across the restaurant world, and inspired some cracking spin-offs.
He was the father of modern yellow journalism, as the elder Bennett was of the earlier type, and he has had a vast influence in creating the character of the press of to-day, a mixture of good and evil qualities, with the evil rather dominating.
The diesel fuel price is calculated by considering the lower heating value.r As [7] (page 318)shows, the different rates of interest have a vast influence on the competitiveness of renewable energy generation units with their comparably high investment costs.
User-generated content has a huge influence over the vast majority of consumers.
That might be taken as a depressing valedictory for a politician who has squandered a vast influence.
And obviously, New York has a vast history of swing influenced music.
He has a vast repertoire of voices.
Nepal has a vast theoretical hydroelectric potential.
More suggestions(14)
has a great influence
has a widespread influence
has a considerable influence
has a significant influence
has a vast impact
has a broad influence
has a substantial influence
has a wide ranging influence
has an enormous influence
has an extensive influence
has a large influence
has a wide influence
has a massive influence
given the vast influence
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com