I'd like to move my washer and dryer from its current location on the main floor to my unfinished basement. Rather than placing it directly below its current location, I've identified a spot on the other end of the house, which happens to be underneath a powder room. Therefore, I will have access to the plumbing for any and all water/drainage needs. My question though, is how can I vent the dryer. I do have access to an exterior wall (concrete/brick), but am curious to know if there is another way to vent it. If I'm forced to vent it outside, is there an easy wasy to cut through the masonery? Any suggestions would be appreciated.

Are the floor joists open? The floor joist should be resting on the concrete basement walls. If you take the exhaust piping up between the joists, you should only have to go through the brick. That's fairly easy to do. Use a 4 lb sledge hammer and a 16" length of ¾” iron pipe to make a hole in the center of what will be a 4" hole. Then enlarge the hole to the required 4" using the pipe and chisels.

If you try to go thru an 8 or 10" concrete wall you will need a small pneumatic jackhammer or a core boring drill.

Like HK siad, it should be fairly easy to install a new vent from your basement. If you cannot, they make ventless dryers that turn the exhaust into water and discharge it into a drain, or there is such a thing as an interior vent which does not require running a duct to the outside, but I don't recommend that as they tend to add humidity to your basement and house.

I think the two guys ahead of me covered your question but I have one for you regarding your plumbing. Just because you are below a powder room doesn't insure you can have a drain. Where does the sewer pipe leave your house, how close and at what level or elevation?