Which expression is equivalent to 3x2y3z

Question

?(1 point)
Responses

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

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

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

xy⋅3yz

Answer 1

To determine which expression is equivalent to \( 3x^2y^3z \), let's start by rewriting it in a clearer form. The expression can be expressed as:

\[ 3 \cdot x^2 \cdot y^3 \cdot z \]

Now, let's analyze each of the provided responses:

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

   • This expands to \( x^2y \cdot 3y^2z \) which equals \( 3x^2y^3z \). This is equivalent!

2. Response 2: \( xy^3 \cdot yz \cdot 3x \)

   • This expands to \( 3x^2y^4z \), which is not equivalent.

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

   • This expands to \( 3x^2y^3z^2 \), which is not equivalent.

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

   • This expands to \( 3xy^2z \), which is not equivalent.

The only expression that is equivalent to \( 3x^2y^3z \) is Response 1: \( x^2y \cdot 3yz \cdot y \).