To apply the property of negative integer exponents, we can start with the expression you mentioned: \(\frac{5^{-9}}{4^{-12}}\).
Using the rule of negative exponents, \(a^{-n} = \frac{1}{a^n}\), we can rewrite the expression with positive exponents:
\[ \frac{5^{-9}}{4^{-12}} = \frac{1}{5^9} \div \frac{1}{4^{12}} = \frac{4^{12}}{5^9} \]
This means that the expression is equivalent to:
\[ \frac{4^{12}}{5^9} \]
Thus, \( \frac{4^{12}}{5^9} \) is the expression equivalent to the original expression with negative exponents, rewritten using positive exponents.