jmc

In order to evaluate the first half of the expression, we must first find $\lceil \frac{3}{2}\rceil$ and then square that integer. We know that $\lceil \frac{3}{2}\rceil =2$, so ${\lceil \frac{3}{2}\rceil }^2=4$. For the second half of the expression, we must first evaluate ${\left(\frac{3}{2}\right)}^2$, and then find the smallest integer greater than or equal to that value. We know that ${\left(\frac{3}{2}\right)}^2=\frac{9}{4}$, so $\lceil {\left(\frac{3}{2}\right)}^2\rceil =\lceil \frac{9}{4}\rceil =3$. Thus, the original expression is just equal to $4+3=\boxed{7}$.