"exploit the fact" is a correct and usable phrase in written English.
It means to take advantage or make use of a particular fact or situation. Example: The marketing team decided to exploit the fact that their product was made with all-natural ingredients in their advertising campaign.
One tactic is to exploit the fact that machines are often faster than humans.
Featural writing systems exploit the fact that even phonemes are not the most fundamental units of analysis of speech.
They were lucky, she says; the show didn't exploit the fact that "we were really green about the business.
Companies are also moving to exploit the fact that millions of people have published information about themselves on the Web.
These exploit the fact that gravitational waves should cause space to stretch in one direction and shrink in the dimension at right angles to it.
Foveon sensors, which can be found in Sigma digital single-lens-reflex (SLR) cameras, cleverly exploit the fact that different wavelengths of light penetrate silicon to different depths.
They exploit the fact that a significant fraction of a neutron's kinetic energy can be transferred to the nucleus that it strikes, producing an energetic recoil nucleus.
Card games typically exploit the fact that each player can identify only the cards he holds, not those of his opponents.
At the same time, other plants apparently began to exploit the fact that primitive gall-forming insects visited the flowers to deposit eggs.
And there are still thousands of pieces of Android malware about which exploit the fact that nobody really understands why apps are so demanding in permissions.
"When my father's father, Joe Sr., would compliment his wife, Esther, he would exploit the fact that she didn't speak much English," he said.
