Answer
$\frac{25}{36}$
Work Step by Step
First, we will simplify the expression within the parenthesis by finding the least common denominator:
$(\frac{1}{2}+\frac{1}{3})^{2}$
=$(\frac{1(3)+1(2)}{6})^{2}$
=$(\frac{3+2}{6})^{2}$
=$(\frac{5}{6})^{2}$
Next, we raise both the numerator and the denominator to the power of $2$ and simplify:
$(\frac{5}{6})^{2}=\frac{5^{2}}{6^{2}}=\frac{5\times5}{6\times6}=\frac{25}{36}$
