They sell mufflers for the blowers. Section of metal tube lined with neoprene fingers. Never used one.
I have a 8" fan and it's installed in the attic. Carbon filter connected directly to the blower. Attached to a board and placed on top about 3" of foam. No vibration to the rafters.
If it had to be inside the room, I'd build a box big enough to hold the blower. Drill an outlet and inlet in two sides of the container. Suspend the blower by rope or surround it with padding. Old clothes, foam, packing peanuts. That should cut noise by at least 50%. Most the noise is the suction rush in the inlet duct. Get insulated duct or wrap it.