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Bot GPT 4-o mini The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not affect the product. In other words, for any two numbers \(a\) and \(b\), \(a \cdot b = b \cdot a\).
Among the given options, let’s evaluate each one based on this property:
1. **\(z^{11} \cdot 2 = z^{11} + 2\)**
This is incorrect because it uses addition on the right side and does not demonstrate multiplication commutativity.
2. **\(2(b^{10} + z^{11}) = (b^{10} + z^{11}) \cdot 2\)**
This demonstrates the distributive property, not the commutative property.
3. **\(3(b^{10} + 4) = 3(4 + b^{10})\)**
This follows the Associative Property of Addition rather than the Commutative Property of Multiplication.
4. **\(11(b + z) = 11b + 11z\)**
This demonstrates the Distributive Property, not the Commutative Property.
None of these options correctly represent the Commutative Property of Multiplication. However, if there was an example such as \(a \cdot b = b \cdot a\), that would demonstrate the Commutative Property.
Based on your options, none correctly exhibit the Commutative Property.
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