If I am a Realtor that acts as an independent contractor, am I able to write off the fees that I have to pay a broker on every transaction I do?

Yes.  That would be deductible in your line of work.  There is an entry on the Schedule C for Commissions and Fees.  These payments qualify.

Thank you very much.  We asked in class, but the answer was not very straight forward.  I don't think the instructor knew...

You're welcome.