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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 mathematical terms, it can be expressed as:
\[ a \cdot b = b \cdot a \]
Let's analyze the options you've provided:
1. \( z^{11} * 2 = z^{11} + 2 \)
- This is incorrect; it does not demonstrate any property of multiplication but rather mistakenly equates multiplication with addition.
2. \( 3(b^{10}+4)=3(4+b^{10})3 \)
- This expression seems to be mistyped. However, if we interpret it correctly, it doesn’t demonstrate the commutative property since it's not merely rearranging factors.
3. \( 2(b^{10}+z^{11})=(b^{10}+z^{11}) * 2 \)
- This represents the Distributive Property, not the Commutative Property.
4. \( 11(b+z)=11b+11z \)
- This statement represents the Distributive Property as well.
None of the provided options clearly illustrate the Commutative Property of Multiplication. If any were meant to simply switch operands in multiplication with no additional operations, that would be a suitable demonstration.
A correct example of the Commutative Property would be:
\( 3 \cdot 4 = 4 \cdot 3 \)
If you need further clarification or examples, let me know!