Exercise 16.13 [kmax-exercise]

Let continuous variables $X_1,\ldots,X_k$ be independently distributed according to the same probability density function $f(x)$. Prove that the density function for $\max{X_1,\ldots,X_k}$ is given by $kf(x)(F(x))^{k-1}$, where $F$ is the cumulative distribution for $f$.