Question

Multiply Linear Expressions Quick Check
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Question
Apply properties of operations to multiply 5a2b5c3⋅−4a7c5
.(1 point)
Responses

20a14b5c15
20 a superscript 14 baseline b superscript 5 baseline c superscript 15 baseline

−20a14b5c15
negative 20 a superscript 14 baseline b superscript 5 baseline c superscript 15 baseline

20a9b5c8
20 a superscript 9 baseline b superscript 5 baseline c superscript 8 baseline

−20a9b5c8
negative 20 a superscript 9 baseline b superscript 5 baseline c superscript 8 baseline
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Answer 1

To multiply the linear expressions \( 5a^2b^5c^3 \) and \( -4a^7c^5 \), we can follow the properties of exponents and multiplication:

1. **Coefficients:** Multiply the numerical coefficients:
\[
5 \times -4 = -20
\]

2. **\(a\) Terms:** Add the exponents of \(a\):
\[
a^2 \times a^7 = a^{2+7} = a^9
\]

3. **\(b\) Terms:** Since \(b^5\) is the only \(b\) term, it remains:
\[
b^5
\]

4. **\(c\) Terms:** Add the exponents of \(c\):
\[
c^3 \times c^5 = c^{3+5} = c^8
\]

Now, combining all these results, we get:
\[
-20a^9b^5c^8
\]

The final answer is:
\[
\text{−20 } a^9 b^5 c^8
\]

So the correct response is:
**−20a^9b^5c^8**.