"exert a significant influence" is correct and usable in written English.
You can use it when discussing the effect or power that someone or something has on something else. For example: "The mayor's words exerted a significant influence on the outcome of the election."
Even dogs exert a significant influence on the tiny life-forms living on our pillows and television screens.
These variables were found to exert a significant influence on the microstructure.
Pre-existing structures within crystalline basement may exert a significant influence over the evolution of rifts.
Binding affinity can exert a significant influence on both the equilibrium and the dynamic response characteristics of such a biosensor.
Peers and the adolescent subculture, as opposed to parents, should exert a significant influence on the dating behavior of Chinese youth.
Correlation between gas and electric loads was also investigated, and was shown to exert a significant influence on the probabilistic results.
You can actually exert a significant influence over the content and tone of letters that are sent out on your behalf.
Minor amounts of both substances are shown to exert a significant influence on the growth process, leading to the formation of predominantly flower-like spherulitic aggregates.
This contribution will demonstrate that the mirror material choice can exert a significant influence on the relative importance of erosion/redeposition affecting the mirror reflectivity.
Tillage system failed to exert a significant influence on any of the indexes studied except grain N content, which was higher under CT than under NT.
Spontaneous regression (SR) of a malignant tumor is defined as a partial or complete disappearance of a tumor without treatment or in response to a treatment that is considered inadequate to exert a significant influence on neoplastic disease [1].
