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

To analyze which expressions are equivalent using the Associative Property, we will first explore how the Associative Property applies. This property allows us to group numbers in different ways without changing the result of multiplication or addition.

Let's consider the original expression:

\[
-3 \cdot (4x \cdot -2) \cdot -6y
\]

Now, let's evaluate each expression one by one:

1. **Evaluate the first expression:**
\[
(-3 \cdot 4x) \cdot (-2 \cdot -6y)
\]
This applies the Associative Property. We can calculate each part:
\[
-3 \cdot 4x = -12x, \quad -2 \cdot -6y = 12y
\]
Thus, the expression simplifies to:
\[
(-12x) \cdot 12y = -144xy
\]

2. **Evaluate the second expression:**
\[
(-3 \cdot 4x) \cdot -2 \cdot -6y
\]
Here, we can similarly group:
\[
(-3 \cdot 4x) = -12x \quad \Rightarrow \quad -12x \cdot -2 = 24x
\]
Now, multiplying this by \(-6y\):
\[
24x \cdot -6y = -144xy
\]

3. **Evaluate the third expression:**
\[
18 - 8x
\]
This expression is not in the same format and doesn't involve the terms from our original product.

4. **Evaluate the fourth expression:**
\[
-7xy
\]
Like the third, this does not match the structure of our original expression.

From our evaluations:

- The first and second expressions evaluated to \(-144xy\), so they are equivalent.
- The third expression \(18 - 8x\) and the fourth expression \(-7xy\) do not match the original expression's structure and aren't equivalent either.

**Conclusion: The equivalent expressions are:**

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

Both expressions appear to be equivalent to the original expression using the Associative Property.