To determine which of the given options is a correct application of the commutative property of multiplication, let's recall what the commutative property states. The commutative property of multiplication tells us that the order in which we multiply two numbers does not affect their product. Mathematically, this is expressed as:
[tex]\[ a \cdot b = b \cdot a \][/tex]
Now, let's analyze the given options one by one to see which one correctly demonstrates this property:
1. [tex]\((-5) \cdot 8 = - (5 \cdot 8)\)[/tex]
This option does not involve changing the order of multiplication but rather applies the distributive property.
2. [tex]\((-5) \cdot 8 = (-8) \cdot 5\)[/tex]
This option changes both the order and the signs of the numbers, which is not simply the commutative property.
3. [tex]\((-5) \cdot 8 = 8 \cdot (-5)\)[/tex]
This option correctly changes the order of the multiplication without altering the numbers, precisely demonstrating the commutative property.
4. [tex]\((-5) \cdot 8 = 5 \cdot (-8)\)[/tex]
This option changes both the order and the signs of the numbers, again not a simple application of the commutative property.
Based on this analysis, the correct application of the commutative property of multiplication is:
[tex]\[ (-5) \cdot 8 = 8 \cdot (-5) \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{3} \][/tex]
