Final answer:
Chitin is the substance in an arthropod's exoskeleton that repels water, forming a hard protective layer while maintaining water-resistant properties.
Step-by-step explanation:
The substance that makes an arthropod's exoskeleton repel water is chitin. Chitin is a nitrogen-containing polysaccharide, composed of repeating units of N-acetyl-ß-d-glucosamine, which is a modified sugar. This material is what forms the hard outer exoskeleton of arthropods, including insects and crustaceans. Not only does chitin provide strength and protection, but it also contributes to the water-repelling properties of the exoskeleton due to its structure and the presence of a waxy, water-resistant layer known as the epicuticle that covers the chitinous procuticle.