Beta carotene is a type of antioxidant from the carotenoid group that can actually protect your skin from sun damage, and sweet potatoes are a particularly rich source of it. You can’t necessarily skip using sunscreen if you are going to be outside for a significant amount of time, but a diet rich in beta carotene increases the time that you can spend in the sun without burning.
Sunburn is important to avoid, not only because it increases your risk of skin cancer, but because it results in cell death. That causes dry and wrinkly skin. If you need yet another reason to eat your sweet potatoes, that beta carotene can impart a warm, bronze tone to your skin without any sun exposure at all.