If you can't find them, they also have vending machines in the laundry rooms where you can purchase detergent, so don't worry if you can't find any. You can also get some powder and put some in ziplocks, that should work too.
Even though it's a little more expensive, I just buy my supplies on the ship. By the time I'm done packing the essentials, a lot of the little things (like detergent) just won't fit in the suitcases--!
The ships sell packages of detergent and liquid fabric softner at least bring dryer sheets cause I forgot them then had to wait for the rinse cycle to pour it in, not something you want to waste time with on a cruise. If you can't find the tablets,( Purex makes them also )I would use the zip lock bag method with powdered detergent you will also need $2.00 in quarters to wash and another $2.00 to dry if your on Carnival.
i bring a small plastic bottle filled with my liquid detergent, i need to by the unscented, "free" type detergent and they don't have that on the ship. The choice of detergents in the vending machines on the ship is very limited so if you have to have a certain type of detergent it would be a good idea to bring your own.