To apply the property of negative integer exponents and rewrite the expression \( \frac{5^{-9}}{4^{-12}} \) with positive exponents only, we can use the rule that states \( a^{-n} = \frac{1}{a^n} \).
- Rewrite \( 5^{-9} \) as \( \frac{1}{5^{9}} \).
- Rewrite \( 4^{-12} \) as \( \frac{1}{4^{12}} \).
So the expression \( \frac{5^{-9}}{4^{-12}} \) can be transformed as follows:
\[ \frac{5^{-9}}{4^{-12}} = \frac{1}{5^{9}} \div \frac{1}{4^{12}} = \frac{1}{5^{9}} \cdot \frac{4^{12}}{1} = \frac{4^{12}}{5^{9}}. \]
Therefore, the expression \( \frac{5^{-9}}{4^{-12}} \) is equivalent to \( \frac{4^{12}}{5^{9}} \) with positive exponents only.