which of the following correctly demonstrates the use of the commutative property of multiplication?(1 point)responses2(b10+z11)=(b10+z11)⋅22 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 23(b10+4)=3(4+b10)33 left parenthesis b superscript 10 baseline plus 4 right parenthesis equals 3 left parenthesis 4 plus b superscript 10 baseline right parenthesis 3z11⋅2=z11+2z superscript 11 baseline times 2 equals z superscript 11 baseline plus 211(b+z)=11b+11z

Answer 1

The commutative property of multiplication states that the order in which two numbers are multiplied does not change the product. In other words, \( a \times b = b \times a \).

To determine which of the options correctly demonstrates the commutative property of multiplication, let's analyze each response:

1. \(2(b^{10}+z^{11})=(b^{10}+z^{11})\cdot 2\)
   This correctly demonstrates the commutative property because it shows that multiplying \( (b^{10} + z^{11}) \) by 2 is the same as multiplying 2 by \( (b^{10} + z^{11}) \).

2. \(3(b^{10}+4)=3(4+b^{10})\)
   This does not clearly demonstrate the commutative property because it is more about the associativity of addition and multiplication, not strictly multiplication.

3. \(3(b^{10}+4)=3(4+b^{10})\)
   Similar to the previous one, this concerns the rearrangement of terms in addition, rather than multiplication as defined by the commutative property.

4. \(3z^{11}\cdot 2=z^{11}+2z^{11}\)
   This equation is incorrect in context as it does not represent the commutative property.

5. \(11(b+z)=11b+11z\)
   This shows the distributive property rather than the commutative property.

Based on this analysis, the correct response demonstrating the use of the commutative property of multiplication is:

Response 1: \(2(b^{10}+z^{11})=(b^{10}+z^{11})\cdot 2\).