The Commutative Property of Multiplication states that changing the order of the factors does not change the product. In other words, \( a \cdot b = b \cdot a \).
Let's analyze the given options:
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Option 1: \( 11(b + z) = 11b + 11z \)
- This demonstrates the Distributive Property, not the Commutative Property.
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Option 2: \( 2(b^{10} + z^{11}) = (b^{10} + z^{11}) \cdot 2 \)
- This shows that the order of multiplication does not affect the product, which is an example of the Commutative Property.
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Option 3: \( z^{11} \cdot 2 = z^{11} + 2 \)
- This is incorrect as it does not hold true mathematically; it shows an incorrect operation.
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Option 4: \( 3(b^{10} + 4) = 3(4 + b^{10}) \)
- This demonstrates that changing the order in which you add \( b^{10} \) and \( 4 \) does not change the sum (which is the Associative Property of Addition), along with the Commutative property of multiplication (since you can rewrite it as \( 3 \cdot (4 + b^{10}) \)).
From the above explanations, Option 2 \( 2(b^{10} + z^{11}) = (b^{10} + z^{11}) \cdot 2 \) is the best example demonstrating the Commutative Property of Multiplication.