Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5 superscript −9 / 4 superscript −12
with positive exponents only.

Enter your answer as a fraction in simplest form.

(1 point)

Answer 1

To simplify the expression \( \frac{5^{-9}}{4^{-12}} \) using the property of negative integer exponents, we can convert the negative exponents to positive.

The property of negative exponents states that \( a^{-n} = \frac{1}{a^n} \). Therefore, we can rewrite the expression as follows:

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

Now, we combine the expressions:

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

This is now an expression with positive exponents. We can leave the final answer as:

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

Next, we can simplify this fraction if possible. Since \( 4^{12} = (2^2)^{12} = 2^{24} \), we can write:

\[
\frac{4^{12}}{5^9} = \frac{2^{24}}{5^9}
\]

Thus, the final answer is:

\[
\frac{4^{12}}{5^9} = \frac{2^{24}}{5^9}
\]

But since the problem asked for it as a fraction in simplest form, we can keep it as:

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

So the final answer is:

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