Which expression is equivalent to 3x2y3z3x2y3z ?(1 point) Responses x2y2z2⋅3yx2y2z2⋅3y x squared y squared z squared times 3 y xy⋅3yzxy⋅3yz x y times 3 y z xy3⋅yz⋅3xxy3⋅yz⋅3x x y cubed times y z times 3 x x2y⋅3yz⋅y

1 answer

To simplify the expression \( 3x^2y^3z^3x^2y^3z \), we first rearrange it by grouping similar terms.

  1. Identify and combine the like terms:

    • Coefficients: \( 3 \) (remaining as it is)
    • For \( x \): \( x^2 \cdot x^2 = x^{2+2} = x^4 \)
    • For \( y \): \( y^3 \cdot y^3 = y^{3+3} = y^6 \)
    • For \( z \): \( z^3 \cdot z = z^{3+1} = z^4 \)
  2. Now, combine everything together: \[ 3x^4y^6z^4 \]

Now, looking at the responses given, we want to find an expression that simplifies to \( 3x^4y^6z^4 \). Let's analyze:

  • Response 1: \( x^2y^2z^2 \cdot 3y \) does not equal \( 3x^4y^6z^4 \).
  • Response 2: \( xy \cdot 3yz \) does not match.
  • Response 3: \( xy^3 \cdot yz \cdot 3x \) does not match.
  • Response 4: \( x^2y \cdot 3yz \cdot y \) does not match.
  • Response 5: \( x^2y \cdot 3yz \cdot y \) does not match.

None of the provided responses seem to simplify to \( 3x^4y^6z^4 \).

Thus, let's double-check:

  • If derived terms mismatch in coefficients or powers of \( x, y, z \), confirm that the combination yields \( 3x^4y^6z^4\) accurately and check individual term responses.

Moving on, if you have further text context that contains the right responses, aligning would be particularly beneficial for exact cross-verification!

As the provided options above do lean towards incorrect simplification, it’s paramount to confirm against more finalized text if able.