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

Question

Responses

z11⋅2=z11+2
z superscript 11 baseline times 2 equals z superscript 11 baseline plus 2

3(b10+4)=3(4+b10)3
3 left parenthesis b superscript 10 baseline plus 4 right parenthesis equals 3 left parenthesis 4 plus b superscript 10 baseline right parenthesis 3

2(b10+z11)=(b10+z11)⋅2
2 left parenthesis b superscript 10 baseline plus z superscript 11 baseline right parenthesis equals left parenthesis b superscript 10 baseline plus z superscript 11 baseline right parenthesis times 2

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

Answer 1

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. In other words, \( a \cdot b = b \cdot a \).

Looking at the options provided:

1. \( z^{11} \cdot 2 = z^{11} + 2 \): This is incorrect because it incorrectly equates multiplication and addition.

2. \( 3(b^{10}+4)=3(4+b^{10}) \): This illustrates the Commutative Property of Addition since it rearranges the terms inside the parentheses, but it doesn't apply to multiplication as a whole.

3. \( 2(b^{10}+z^{11})=(b^{10}+z^{11}) \cdot 2 \): This demonstrates the Commutative Property of Multiplication, as it shows that multiplying by 2 can be applied to the expression in either order.

4. \( 11(b+z)=11b+11z \): This demonstrates the Distributive Property, not the Commutative Property.

Based on these analyses, the correct response that demonstrates the use of the Commutative Property of Multiplication is \( 2(b^{10}+z^{11})=(b^{10}+z^{11}) \cdot 2 \).