wow, woah on the dish soap, and the tick powder. NONO that's waaaay to harsh. I've had friends that did that and the end result wasn't good. A warm water bath with couple drops of betadine in it is perfectly fine. By now you already have the p.a.m. so your probably already good. But, nono tick powder and dish soap is way too harsh and can cause u.r.i. and other respiratory problems. I've treated mites before they are gross but nothing to freak out about.
Let me clarify that. I put the flea and tick powder in the plastic bag with the used paper towels that had mites on them and were being thrown out. Not with the snake. And the dishwashing soap was about 4 or 5 drops that was mixed in with about 4 gallons of water...