Final answer:
The smallest prime number greater than 21 is 23, and the largest prime number less than 16 is 13, therefore xy is 23 multiplied by 13, equalling 299.
Step-by-step explanation:
If x is the smallest prime number greater than 21 and y is the largest prime number less than 16, then to find the value of xy, we need to determine the actual values of x and y. The smallest prime number greater than 21 is 23 since 22 and 23 are the only two numbers to consider, and 22 is not prime. The largest prime number less than 16 is 13, as the prime numbers less than 16 are 2, 3, 5, 7, 11, and 13.
Therefore, x = 23 and y = 13.
The product of x and y (xy) is 23 multiplied by 13, which equals 299.