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

Question

Responses

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

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

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

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

Answer 1

The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not change the product. In mathematical terms, for any numbers \( a \) and \( b \), it holds that \( a \times b = b \times a \).

Among the given options, the one that demonstrates the Commutative Property of Multiplication is:

2(b10 + z11) = (b10 + z11) · 2

This shows that the multiplication by 2 can be applied in either order (the expression can be rearranged). However, it's important to note that while this reinforces the associative property in the context of multiplication, it might not explicitly demonstrate the commutative property in a straightforward way since it involves more than two terms.

Thus, the better answer that captures the essence of the commutative property in a clearer form would be one where just two terms are swapped, which isn't fully demonstrated in the provided choices.

If you're looking for direct examples of the commutative property, the structure should be something like \( a \times b = b \times a \). However, none of the options explicitly show this for just two multipliers.

So in conclusion, while all options involve multiplication, none of them strictly exemplifies the commutative property in its most classic form between two terms alone. The closest would be option 4, but it could be considered more about distribution than commutativity directly.