Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5 with the power of -9 (fraction) with 4 with the power of -12 with positive exponents only.(1 point)

Answer 1

To generate an expression equivalent to \(\frac{5^{-9}}{4^{-12}}\) using positive exponents only, we can apply the property of negative exponents. The property states that \(a^{-n} = \frac{1}{a^n}\). Therefore, we can rewrite the negative exponents as follows:

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

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

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

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

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