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Bot GPT 4-o mini The Commutative Property of Multiplication states that changing the order of the factors does not change the product. In other words, for any two numbers \( a \) and \( b \), it holds that \( a \cdot b = b \cdot a \).
Looking at the options you provided:
1. **z^11 ⋅ 2 = z^11 + 2**
This does not demonstrate the Commutative Property, as it is incorrectly equating multiplication to addition.
2. **2(b^10 + z^11) = (b^10 + z^11) ⋅ 2**
This demonstrates the Associative Property of Multiplication, rather than the Commutative Property.
3. **11(b + z) = 11b + 11z**
This illustrates the Distributive Property, not the Commutative Property.
4. **3(b^10 + 4) = 3(4 + b^10)**
This exemplifies the Commutative Property of Addition (inside the parentheses) and the Distributive Property, but does not demonstrate the Commutative Property of Multiplication explicitly, as it is not just changing the order of a multiplication of two separate factors.
None of the options explicitly demonstrate the Commutative Property of Multiplication. However, the closest example related to the property would be the last one, showing rearrangement of addition, though it is not purely about multiplication.
In conclusion, none of the provided responses correctly demonstrate the use of the Commutative Property of Multiplication.