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So the soffit sits flush to the wall, you may need to notch out the soffit for the vent. First mark the vent location on the soffit. Then cut the soffit frame with a reciprocating saw, being careful not to cut into the drywall. To notch out the soffit for the vent so it sits flush with the wall, first mark off the vent location. Then cut the frame with a reciprocating saw, being careful not to cut into the drywall. Use a prybar to pull out the notched piece.
Center and attach the mounting plate to the soffit with screws, and then attach the hood.
Screw the transition piece for the vent into the mounting bracket and attach the vent elbow.
Note: The size of the vent is determined by the cubic feet per minute (CFM). The higher the CFM, the larger the vent.
Seal the seams of the vent and the elbow with aluminum tape.
Finish by covering the framing of the vertical soffit with 1/2" plywood, secured with standard drywall screws. You can the plywood with tiles for a decorative touch.