problem: Evaluate $\left\lceil\left(\frac{7}{4}\right)^2\right\rceil^2$
solution: Because $\left(\frac{7}{4}\right)^2$ equals $\frac{49}{16}$, the expression can be rewritten as $\left\lceil\frac{49}{16}\right\rceil^2$. The smallest integer greater than $\frac{49}{16}$ is $4$, and $4^2=\boxed{16}$.