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