In 1918, Hardy and Ramanujan published a seminal paper which included an asymptotic formula for the partition function. In their paper, they also state without proof an asymptotic equivalence for the number of partitions of a number into $k$-th powers. In this talk, I will present an asymptotic formula for the number of partitions into $k$-th powers using a relatively simple method, verifying the claim of Hardy and Ramanujan. We will then discuss extensions of this result to partitions into integer values of polynomials.