The preferred form of the adjective meaning tending to make use of selfishly or unethically is exploitative, not exploitive. This preference is shown across all main varieties of English.
Exploitive may seem breezier and more efficient, but English often flouts economy when it comes to the -tative and -tive suffixes. A few dictionaries accept exploitive as an alternative spelling of exploitative, but most correctly acknowledge that the latter is the far more common form.
The following ngram, which graphs the use of exploitive and exploitative (as a percentage of all words used) in a large number of English-language works published in the 20th century, shows that the longer form is now preferred by a huge margin:
Edited publications generally prefer exploitative to exploitive. In current news sources, for instance, the ratio is about 20 to one. Here are a few examples of the word in action:
So here we have an exploitative company, Verizon, channeling its income to another corrupt partner in Britain, all in the name of avoiding taxation. [The Nation]
She covered exploitative sales techniques used by funeral directors, such as the meticulous arrangement of coffins to exploit the most from consumers. [Guardian]
No more Picktons and no more exploitative pimps. [Winnipeg Free Press]
First, commercial surrogacy can be exploitative because the contracting parties are not always free and equal. [Sydney Morning Herald]