To apply the property of negative integer exponents, we can use the rule that states:
\[ a^{-n} = \frac{1}{a^{n}} \]
This means that we can convert negative exponents to positive exponents by taking the reciprocal.
Let's apply this to \(5^{-9}/4^{-12}\):
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Convert \(5^{-9}\) to positive exponent: \[ 5^{-9} = \frac{1}{5^9} \]
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Convert \(4^{-12}\) to positive exponent: \[ 4^{-12} = \frac{1}{4^{12}} \]
Now, rewrite the expression \(5^{-9}/4^{-12}\):
\[ \frac{5^{-9}}{4^{-12}} = \frac{\frac{1}{5^9}}{\frac{1}{4^{12}}} \]
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ = \frac{1}{5^9} \times 4^{12} = \frac{4^{12}}{5^9} \]
Thus, we can write the expression with positive exponents only:
\[ 5^{-9}/4^{-12} = \frac{4^{12}}{5^9} \]
So fill in the blank:
\[ 5^{-9}/4^{-12} = \frac{4^{12}}{5^9} \]
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