Which of the following correctly demonstrates the use of the Commutative Property of Multiplication? (point) z ^ 11 * 2 = z ^ 11 + 2; 2(b ^ 10 + z ^ 11) = (b ^ 10 + z ^ 11) * 2; 3(b ^ 10 + 4) = 3(4 + b ^ 10) * 3; 11(b + z) = 11b + 11z

1 answer

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. In other words, \( a \times b = b \times a \).

Looking at the options you've provided:

  1. \( z^{11} * 2 = z^{11} + 2 \) - This is incorrect. It does not demonstrate multiplication at all.

  2. \( 2(b^{10} + z^{11}) = (b^{10} + z^{11}) * 2 \) - This correctly demonstrates the Commutative Property of Multiplication, as it shows that multiplying the expression by 2 can be done in either order.

  3. \( 3(b^{10} + 4) = 3(4 + b^{10}) * 3 \) - This does not correctly demonstrate the commutative property due to the repetition of \( * 3 \) on the right side, and it's not clear it illustrates commutativity.

  4. \( 11(b + z) = 11b + 11z \) - This demonstrates the Distributive Property, not the Commutative Property.

Therefore, the correct choice that demonstrates the use of the Commutative Property of Multiplication is:

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