Use the Associative Property to determine which expressions are equivalent.(1 point) Responses

To determine which expressions are equivalent using the Associative Property, we need to recognize that the Associative Property allows us to regroup terms in multiplication without changing the product. That is, \( a \cdot (b \cdot c) = (a \cdot b) \cdot c \).

Let's analyze the given expressions one by one:

1. **Expression:** \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot (-2 \cdot -6y)\)
- This is a correct use of the Associative Property. By regrouping, we can see that this expression is equivalent.

2. **Expression:** \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 \cdot -6y\)
- This is also a correct use of the Associative Property, and it simplifies to the same expression.

3. **Expression:** \(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\)
- This equation is not equivalent because the left side is a product involving variables, while the right side is a separate expression (a linear expression without \(y\)). Therefore, this expression is not equivalent.

4. **Expression:** \(-3 \cdot (4x \cdot -2) \cdot -6y = -7xy\)
- This equation is also not equivalent. The left side is a multiplication of three terms, while the right side is a simplified expression involving different constants and variables. Hence, this expression is not equivalent.

### Summary:
The expressions that are equivalent using the Associative Property are:

1. \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot (-2 \cdot -6y)\)
2. \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 \cdot -6y\)

The last two expressions do not hold equivalence.