Identify the property of integers being illustrated in each of the following:

a:(-2)(3) �¸ I
b: (-4)0=0
c: -2(3+4)=-2(3) + (-2)4
d: (-2)3=3(-2)

simplify this expression -5(10+7m)

To identify the property of integers being illustrated in each of the given examples, let's break down the calculations step by step:

a: (-2)(3) ≠ I
In this example, the property being illustrated is the closure property of integers under multiplication. The property states that if you multiply two integers, the result is always an integer.

b: (-4)0 = 0
In this case, the property being illustrated is the zero property of multiplication. According to this property, any number multiplied by zero equals zero.

c: -2(3+4) = -2(3) + (-2)(4)
Here, the illustrated property is the distributive property of multiplication over addition. This property states that when you multiply a number by a sum of two other numbers, you can distribute the multiplication to each term inside the parentheses before performing addition or subtraction.

d: (-2)3 = 3(-2)
In this example, the property being illustrated is the commutative property of multiplication. The commutative property states that the order of the factors does not affect the result of multiplication. In other words, when you multiply two numbers, you can swap their positions without changing the product.

By following the explanations above, you can identify the properties of integers being illustrated in each of the given examples.