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Use the Associative Property to determine which expressions are equivalent.(1 point) Responses −3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y) negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals left parenthesis negative 3 times 4 x right parenthesis left parenthesis negative 2 times negative 6 y right parenthesis −3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅

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To determine if the expressions using the Associative Property are equivalent, we can analyze the two expressions:

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

The Associative Property states that the way in which numbers are grouped in multiplication does not change the product. Therefore, we can regroup the factors in either expression.

Let's break down the first expression:

\(-3 \cdot (4x \cdot -2) \cdot -6y\) can be grouped as:

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

Now rearranging the factors:

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

Now moving to the second expression:

\((-3 \cdot 4x) \cdot (-2 \cdot -6y)\) can be expanded, since \(-2\) times \(-6y\) is positive:

\[ = (-3 \cdot 4x) \cdot 12y \]

So both expressions will evaluate to the same product. Since both simplify and yield the same result when factoring, we conclude that:

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

Thus, the expressions are equivalent using the Associative Property.