First thing you need to determine is if its 12V or 120V power in the wire. Forgive me if there is some standard color coding that I'm not familiar with. This could either be 120V for the overhead A/C or 12V. It looks like the vent is currently a passive vent with no powered air movement right?
Do you have a multimeter with pointed probes you can test the voltage? If its 12V DC, you could use a butt splice connector to add a wire for your new fan or you may prefer to have it soldered in and shrink wrapped. Be sure you've killed the power to the wire before you cut it if you choose to go with a butt splice.
I just swapped out a bathroom vent with a Fan-Tastic Fan 6600R and it truly is Fantastic!
Bill & Pam
2003 Damon Daybreak, 8.1 Vortec Jeep Wrangler toad