Marsh Young
05/25/2023 · Junior High School
Apply the Property of Negative Integer Exponents to generate an expression equivalent to \( \frac{5^{-9}}{4^{-12}} \) with positive exponents only. (1 point) \( \frac{5^{-9}}{4^{-12}}=\square \)
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Tutor-Verified Answer
Step-by-step Solution
To apply the property of negative integer exponents, we can use the fact that \( a^{-n} = \frac{1}{a^n} \).
Starting with the expression:
\[
\frac{5^{-9}}{4^{-12}}
\]
We can rewrite the negative exponents as follows:
\[
\frac{5^{-9}}{4^{-12}} = \frac{1}{5^9} \div \frac{1}{4^{12}} = \frac{1}{5^9} \times 4^{12}
\]
Now, when we divide by a fraction, we multiply by its reciprocal:
\[
= 4^{12} \cdot \frac{1}{5^9} = \frac{4^{12}}{5^9}
\]
Thus, the expression with positive exponents only is:
\[
\frac{4^{12}}{5^9}
\]
So, we can write:
\[
\frac{5^{-9}}{4^{-12}} = \frac{4^{12}}{5^9}
\]
The final answer is:
\[
\frac{5^{-9}}{4^{-12}} = \frac{4^{12}}{5^9}
\]
Quick Answer
\[
\frac{5^{-9}}{4^{-12}} = \frac{4^{12}}{5^9}
\]
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