What is 2x2y4z5⋅4x3y5z2

Question

?(1 point)
Responses

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

6x5y9z7
6 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

8x6y20z10

Answer 1

To solve \( 2x^2y^4z^5 \cdot 4x^3y^5z^2 \), we will multiply the coefficients and the variables separately.

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

2. Combine the \(x\) terms: \[ x^2 \cdot x^3 = x^{2+3} = x^5 \]

3. Combine the \(y\) terms: \[ y^4 \cdot y^5 = y^{4+5} = y^9 \]

4. Combine the \(z\) terms: \[ z^5 \cdot z^2 = z^{5+2} = z^7 \]

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

Thus, the answer is:

8x^5y^9z^7

So the correct response is: 8x5y9z7