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