To determine which expression is equivalent to \(3x^2y^3z\), we need to simplify each of the options provided and see which one matches this expression.
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Option 1: \(x^2y^2z^2 \cdot 3y\) \[ = 3y \cdot x^2y^2z^2 = 3x^2y^{2+1}z^2 = 3x^2y^3z^2 \] This is not equivalent to \(3x^2y^3z\).
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Option 2: \(xy^3 \cdot xz \cdot 3x\) \[ = xy^3 \cdot 3x \cdot z = 3x^2y^3z \] This is equivalent to \(3x^2y^3z\).
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Option 3: \(x^2y \cdot 3yz \cdot y\) \[ = 3x^2y \cdot y \cdot z = 3x^2y^{1+1}z = 3x^2y^2z \] This is not equivalent to \(3x^2y^3z\).
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Option 4: \(xy \cdot 3yz\) \[ = 3xy \cdot yz = 3x \cdot y^{1+1} \cdot z = 3xy^2z \] This is not equivalent to \(3x^2y^3z\).
In conclusion, the equivalent expression to \(3x^2y^3z\) is from Option 2: \(xy^3 \cdot xz \cdot 3x\).