To simplify the expression \( \frac{11^{13}}{11^{2}} \), you can use the property of exponents that states:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In this case, applying this property:
\[ \frac{11^{13}}{11^{2}} = 11^{13-2} = 11^{11} \]
So, the simplified form is:
\[ 11^{11} \]