Question

Use the Product Rule of Exponents to simplify the expression (−8)4⋅(−8)5
. Leave your answer in exponential form.

Show your work.

Answer 1

To simplify the expression \((-8)^4 \cdot (-8)^5\) using the Product Rule of Exponents, we can use the following rule:

\[
a^m \cdot a^n = a^{m+n}
\]

In this case, our base \(a\) is \(-8\), \(m\) is \(4\), and \(n\) is \(5\). Applying the Product Rule:

\[
(-8)^4 \cdot (-8)^5 = (-8)^{4+5}
\]

Now, we add the exponents:

\[
4 + 5 = 9
\]

Thus, we have:

\[
(-8)^4 \cdot (-8)^5 = (-8)^9
\]

The final simplified expression in exponential form is:

\[
\boxed{(-8)^9}
\]