This is one of the most prominent red flags
which indicates a bad client, in my opinion.
It's really not that complicated.
Sorry, I do not work pro bono or without payment on request.
There's no need to explain any further.
If they are persistent....
Unfortunately I do not work for free. Like anyone with a mortgage/rent and the desire to eat regularly.... I expect financial compensation for my work. "Exposure" won't pay my bills.
If you are actually open to a barter deal.... Another ploy is to ask then for an equal amount of product/services to your fees.. i.e if they sell dog food and are asking for a $6,000 project to be done only for "exposure", assuming you have a dog... ask them for $6,000 worth of dog food and watch how they waffle and waiver. This only works if they already have a product/service.. never let them agree to give you something "in the future" or "when the product is in production", etc. Because they'll back out or conveniently forget.
You can pretty much forget about "getting a paying client" out of any such request.
If someone offering this proposal had any intention of ever paying for any service, they wouldn't ask you to work for free. If you won't work for "exposure", chances are they will go find some other person who will and take advantage of that person rather than pay you anything. If they tell you they will pay after they see you won't accept "exposure", they'll low-ball the payment or be very slow to pay, or simply promise to pay and never send a check — knowing that chances are you won't legally follow up on any non-payment.
The simple truth is, say "no" and move on. Don't waste your time further. There's no need to negotiate or converse further. Good clients never offer such structures. Seriously, never. Because good clients will value your time and skill and will understand that your abilities are worthy of compensation - even if their budget is low, a client worth speaking with won't ask for anything free. It's one thing for a client to state "that's higher than we can afford" after seeing a quote/estimate. It's an entirely different matter for a client to approach you and ask for something free.
The next red flag would be when they promise you "a lot of work in the future" if you help them out with this project by completing it for "exposure".