Which of the following correctly demonstrates the use of the Commutative Property of Multiplication?(1 point)

Responses

z^11⋅2=z^11+2

2(b^10+z^11)=(b^10+z^11)⋅2

11(b+z)=11b+11z

3(b^10+4)=3(4+b^10)3

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

The Commutative Property of Multiplication states that changing the order of factors does not change the product. In simple terms, for any two numbers \( a \) and \( b \), the property can be expressed as \( a \cdot b = b \cdot a \).

Among the choices provided, let's analyze them:

1. \( z^{11}\cdot2 = z^{11} + 2 \) (Incorrect; this does not demonstrate the property as it involves addition instead of multiplication.)

2. \( 2(b^{10}+z^{11}) = (b^{10}+z^{11}) \cdot 2 \) (This is an example of the Distributive Property, not the Commutative Property.)

3. \( 11(b+z) = 11b + 11z \) (This also demonstrates the Distributive Property, not the Commutative Property.)

4. \( 3(b^{10}+4) = 3(4+b^{10}) \) (This demonstrates the Commutative Property of Addition inside the parentheses but doesn't actually show multiplication itself. However, it rearranges the additive terms' order.)

None of the responses provided directly and clearly demonstrate the Commutative Property of Multiplication as it strictly applies to multiplication.

An example correctly showing the Commutative Property of Multiplication would be \( ab = ba \).

However, from the context and options provided, Option 4 suggests a rearrangement of addition within the parentheses, which indirectly hints at the commutative property (though it is primarily an application of the distributive property). If we must choose one from the options given, it would be Option 4 simply due to its inclusion of a rearrangement, even though it does not clearly exemplify the Commutative Property of Multiplication directly.

Therefore, the most relevant answer based on a loose interpretation within the options is:

**3(b^{10}+4) = 3(4+b^{10})**