Basement bathroom exhaust fan

What are you trying to exhaust?
Moisture (shower or bath) or just a toilet - smell?
How far to an outside wall?

Moisture and smell. It has both shower and toilet. The fan is closer to the toilet side.

sjahan22 said:

I have power vented water heater and I am afraid to tie into that because of backflow concerns.

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There's an excellent chance that would be prohibited by code, and a bad idea for the reason you said.

sjahan22 said:

How and where can I tie this exhaust into

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You might not be able to tie it in anywhere; best bet would be to extend the duct and go out a wall, or through the rim joist if your basement is full depth. (And if code allows you to do that.. you can probably ask the inspector for a recommendation).

Would I be able to tie this into the plumbing vent. I have vent from my sink (in the basement going up and out)

No. You need to run it outside by itself. The only other thing you could tie into would be another exaust fan but then you would need to increase the size of that to the outside.