Bath vent question (with pic)

Hello, I have a question on installation of a bath vent. The bathroom is gutted completely, so I'm installing this bath fan in a joist cavity of the ceiling. If I ran the duct straight within the joist cavity to the outside wall, that actually puts me into the eve rather than just out on the side of the house. I've drawn a picture and put it in the Photos section of this group in a folder called Shane's. I'm wondering how I do this. In the picture, I've drawn it how I think I would install, but how do I access that eve space? Do I have to rip open the soffit? Doesn't seem to easy. I'd appreciate any help. Thanks, Shane