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

Question

Responses

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

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

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

z11⋅2=z11+2

Answer 1

The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not affect the product. In mathematical terms, this can be expressed as \( a \cdot b = b \cdot a \).

Let's analyze the options you provided:

1. \( 2(b^{10} + z^{11}) = (b^{10} + z^{11}) \cdot 2 \)
   This demonstrates the Associative Property of Multiplication, not the Commutative Property.

2. \( 3(b^{10} + 4) = 3(4 + b^{10}) \)
   This shows that addition is being commuted within the parentheses, but it does not specifically demonstrate the Commutative Property of Multiplication.

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

4. \( z^{11} \cdot 2 = z^{11} + 2 \)
   This is not a valid equation and does not represent any property.

None of these options correctly demonstrate the Commutative Property of Multiplication. A simple correct example of the Commutative Property would be \( 2 \cdot 3 = 3 \cdot 2 \).

If you need further clarification or have more questions, feel free to ask!