A power washer works great on a patio slab!
Pressure wash, you may need to use a cleaning solution depending on the current condition. Then use wet & forget outdoor to help keep it clean.
Depending on what types of stains you have on the patio, clean with whatever works best....food or grease, likely a squirt or two of Dawn dish washing soap will solve the problem. Then pressure wash using your house hose turned as high as possible and a plastic scrub brush or maybe it would be worth it to rent a pressure washer for an hour or so to do a real professional job of cleaning the patio slab.