Which of the following correctly demonstrates the use of the Commutative Property of Multiplication?(1 point)%0D%0AResponses%0D%0A%0D%0A2(b10+z11)=(b10+z11)⋅2%0D%0A2 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%0D%0A%0D%0A11(b+z)=11b+11z%0D%0A11 left parenthesis b plus z right parenthesis equals 11 b plus 11 z%0D%0A%0D%0Az11⋅2=z11+2%0D%0Az superscript 11 baseline times 2 equals z superscript 11 baseline plus 2%0D%0A%0D%0A3(b10+4)=3(4+b10)3%0D%0A3 left parenthesis b superscript 10 baseline plus 4 right parenthesis equals 3 left parenthesis 4 plus b superscript 10 baseline right parenthesis 3

Answer 1

The Commutative Property of Multiplication states that the order of the factors can be changed without changing the product. In mathematical terms, this means \( a \times b = b \times a \).

From the options you provided, the correct demonstration of the Commutative Property of Multiplication is:

3(bⁱ⁰ + 4) = 3(4 + bⁱ⁰)

This expression shows that the order of the terms inside the parentheses can be switched, applying the commutative property in the context of addition before multiplication, although it maintains the structure of multiplication throughout. However, if we strictly look for multiplication properties, the change in factors must directly show rearrangement of multiplication alone, such as \( z^{11} \cdot 2 = 2 \cdot z^{11} \).

The first response, 2(bⁱ⁰ + z¹¹) = (bⁱ⁰ + z¹¹)⋅2, does not demonstrate the commutative property of multiplication clearly and directly between multiplicative terms alone.

Thus, while the most straightforward example demonstrating the pure Commutative Property would be \( a \cdot b = b \cdot a \) (which is absent in your options), the chosen option reflects rearrangement that includes multiplication.