Question

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

Answer 1

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

Thus, we can rewrite each term as follows:

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

Now we can combine these expressions:

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

So, the equivalent expression using only positive exponents is:

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