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

Question

with positive exponents only.(1 point)
5^−9/4^−12=

Answer 1

To simplify the expression \( \frac{5^{-9}}{4^{-12}} \) using the property of negative integer exponents, we can apply the following rules:

1. \( a^{-n} = \frac{1}{a^n} \)
2. \( \frac{a^{-m}}{b^{-n}} = \frac{b^n}{a^m} \)

Using these properties, we can rewrite the expression:

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

Now, to express it with only positive exponents:

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

Thus, the expression equivalent to \( \frac{5^{-9}}{4^{-12}} \) with positive exponents is:

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