To find which expression is equivalent to \(3x^{2}y^{3}z\), we'll simplify each provided option and see if it matches the original expression.
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\(x^{2}y^{2}z^{2} \times 3y\) \[ = 3y \cdot x^{2}y^{2}z^{2} = 3x^{2}y^{3}z^{2} \] (Does not match)
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\(xy \times 3yz\) \[ = 3xyz^2 \] (Does not match)
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\(xy^3 \times yz \times 3x\) \[ = 3x \cdot xy^3 \cdot yz = 3x^2y^4z \] (Does not match)
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\(x^{2}y \times 3yz \times y\) \[ = 3y \cdot x^{2}y \cdot yz = 3x^{2}y^{2}z \] (Does not match)
None of the options directly match the expression \(3x^{2}y^{3}z\). However, let's breakdown option 4 by properly considering the number of y's it involves: \[ = 3x^{2}y^2z \cdot y = 3x^{2}y^3z \] This shows that the proper way to group gives us \(3x^{2}y^{3}z\).
Thus, option 4: \(x^{2}y \times 3yz \times y\) is equivalent to \(3x^{2}y^{3}z\).