Which expression is equivalent to 3x2y3z

Question

?(1 point)
Responses

x2y⋅3yz⋅y
x squared y times 3 y z times y

x2y2z2⋅3y
x squared y squared z squared times 3 y

xy3⋅yz⋅3x
x y cubed times y z times 3 x

xy⋅3yz

Answer 1

To find an expression equivalent to \( 3x^2y^3z \), let's analyze each of the provided options and simplify them to see if they equal \( 3x^2y^3z \).

1. Option: \( x^2y \cdot 3yz \cdot y \)

   • Simplifying: \[ x^2y \cdot 3yz \cdot y = 3x^2y \cdot yz \cdot y = 3x^2y \cdot y^2z = 3x^2y^3z \]
   • This is equivalent to \( 3x^2y^3z \).

2. Option: \( x^2y^2z^2 \cdot 3y \)

   • Simplifying: \[ x^2y^2z^2 \cdot 3y = 3x^2y^3z^2 \]
   • This is not equivalent to \( 3x^2y^3z \) (the z exponent is different).

3. Option: \( xy^3 \cdot yz \cdot 3x \)

   • Simplifying: \[ xy^3 \cdot yz \cdot 3x = 3x^2y^4z \]
   • This is not equivalent to \( 3x^2y^3z \) (the y exponent is different).

4. Option: \( xy \cdot 3yz \)

   • Simplifying: \[ xy \cdot 3yz = 3xy^2z \]
   • This is not equivalent to \( 3x^2y^3z \) (the x and y exponents are different).

The only option that simplifies to \( 3x^2y^3z \) is:

Option 1: \( x^2y \cdot 3yz \cdot y \).