To simplify the expression \( \frac{13^{12}}{13^{-10}} \), we use the rule of exponents which states that when dividing like bases, we subtract the exponents:
\[ \frac{a^m}{a^n} = a^{m-n} \]
Applying this to our expression:
\[ \frac{13^{12}}{13^{-10}} = 13^{12 - (-10)} = 13^{12 + 10} = 13^{22} \]
Thus, the simplified expression is:
\[ \boxed{13^{22}} \]