To simplify \( 13^{12} \div 13^{-10} \), you can use the property of exponents that states:
\[ \frac{a^m}{a^n} = a^{m-n} \]
Applying this property, we have:
\[ 13^{12} \div 13^{-10} = 13^{12 - (-10)} = 13^{12 + 10} = 13^{22} \]
So, the simplified form is:
\[ \boxed{13^{22}} \]