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It sounds that just asking and waiting for him to do it has not worked out so far for you.
Perhaps you could set some kind of an ultimatum for him. If you don't do this by_____then I will______(whatever he feels would be a consequence for him)
If he is expecting you to do his laundry that week or cook dinner etc. Whatever it is that he relies on you to do, you halt doing until he does what you asked.
If you see that he is not motivated then let him know that you would want to go to couple's therapy. See if this is a procrastination problem, if he is unmotivated (some people who're depressed display such behavior) Try to think about when this behavior had started on his part (if something had set it off or if he had been like that all along)
He must see that this is upsetting to you and him ignoring it whatever the reason is not a good sign.
Depending on what you need done/fiexed, let him know that if you hire someone else to do it he will have to pay for it.