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

Responses

11(b+z)=11b+11z
11 left parenthesis b plus z right parenthesis equals 11 b plus 11 z

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

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

2(b10+z11)=(b10+z11)⋅2

1 answer

The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not change the product. This can be expressed as \( a \times b = b \times a \) for any numbers \( a \) and \( b \).

Looking at the provided options:

  1. \( 11(b+z) = 11b + 11z \) - This demonstrates the Distributive Property, not the Commutative Property.

  2. \( 3(b^{10}+4) = 3(4+b^{10}) \) - This demonstrates the Commutative Property of Addition inside the parentheses but not the Commutative Property of Multiplication.

  3. \( z^{11} \cdot 2 = z^{11} + 2 \) - This is incorrect because multiplication is being incorrectly expressed as addition.

  4. \( 2(b^{10}+z^{11}) = (b^{10}+z^{11}) \cdot 2 \) - This demonstrates the Commutative Property of Multiplication because it shows that changing the order of multiplication does not change the result.

Therefore, the correct demonstration of the Commutative Property of Multiplication is:

\( 2(b^{10}+z^{11}) = (b^{10}+z^{11}) \cdot 2 \).