Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12
with positive exponents only.(1 point)
5^−9/4^−12=

Remaining Attempts : 3

Answer 1

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

First, we rewrite the expression:

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

Dividing by a fraction is the same as multiplying by its reciprocal:

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

This can be rewritten as:

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

So the expression \( \frac{5^{-9}}{4^{-12}} \) with positive exponents only is:

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