mercilessly, ruthlessly
The workers are ruthlessly exploited by their employers.

cynically
He pursued his own interests, cynically exploiting his privileged position as trustee.

shamelessly
deliberately
sexually

extensively, heavily
fully, to the full (esp. BrE), to the fullest (esp. AmE)
The company has been successful in exploiting new technology to the full.
Birds exploit these wind patterns to the fullest.

further
widely
effectively, profitably, successfully
properly
quickly
easily
cleverly, skilfully/skillfully
The architect has cleverly exploited new materials and building techniques.

commercially
She was eager to exploit her discovery commercially.

be determined to, be keen to (esp. BrE), hope to, seek to
be quick to
The team were quick to exploit their competitive advantage.

attempt to
fail to

Exploit is used with these nouns as the object:
consumer, division, fear, gap, loophole, niche, potential, resource, seam, situation, source, strength, technology, tragedy, vulnerability, weakness, worker