The commutative property of multiplication states that changing the order of the factors does not change the product. In mathematical terms, this can be expressed as \(a \cdot b = b \cdot a\).
Let's analyze each option:
A. \(11(b+z)=11b+11z\)
This demonstrates the distributive property, not the commutative property.
B. \(3(b^{10}+4)=3(4+b^{10})3\)
This is incorrect mathematically and does not demonstrate the commutative property.
C. \(z^{11} \cdot 2 = z^{11}+2\)
This is incorrect; it does not use the commutative property and is mathematically inaccurate.
D. \(2(b^{10} + z^{11}) = (b^{10} + z^{11})2\)
This demonstrates the commutative property of multiplication because it shows that multiplying \(2\) by the expression \((b^{10} + z^{11})\) can be done in either order.
Thus, the correct option that demonstrates the commutative property of multiplication is:
D. \(2(b^{10} + z^{11}) = (b^{10} + z^{11})2\)