Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12

Question

with positive exponents only.(1 point)

Answer 1

To rewrite the expression \( \frac{5^{-9}}{4^{-12}} \) with positive exponents, we can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Starting with the expression:

\[ \frac{5^{-9}}{4^{-12}} \]

We can rewrite this using the property of negative exponents:

\[ = \frac{1}{5^9} \cdot \frac{4^{12}}{1} \]

This simplifies to:

\[ = \frac{4^{12}}{5^9} \]

Now, we have an expression with positive exponents only:

\[ \frac{4^{12}}{5^9} \]

This is the final equivalent expression with positive exponents.