Question

Multiply Linear Expressions Quick Check
2 of 52 of 5 Items
Question
What is 2x2y4z5⋅4x3y5z2
?(1 point)
Responses

6x5y9z7
6 x superscript 5 baseline y superscript 9 baseline z superscript 7 baseline

8x6y20z10
8 x superscript 6 baseline y superscript 20 baseline z superscript 10 baseline

8x5y9z7
8 x superscript 5 baseline y superscript 9 baseline z superscript 7 baseline

8x6y9z7
8 x superscript 6 baseline y superscript 9 baseline z superscript 7 baseline
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Answer 1

To multiply the linear expressions \( 2x^2y^4z^5 \) and \( 4x^3y^5z^2 \), we need to multiply the coefficients and add the exponents for like bases.

1. **Multiply the coefficients:**
\[
2 \cdot 4 = 8
\]

2. **Add the exponents for \(x\):**
\[
x^2 \cdot x^3 = x^{2+3} = x^5
\]

3. **Add the exponents for \(y\):**
\[
y^4 \cdot y^5 = y^{4+5} = y^9
\]

4. **Add the exponents for \(z\):**
\[
z^5 \cdot z^2 = z^{5+2} = z^7
\]

Putting it all together, we get:
\[
8x^5y^9z^7
\]

So, the correct response is:
**8x⁵y⁹z⁷**.