Using the Commutative Property of Multiplication, we can see that this statement is true.
b This time, we have been given the following equation.
a( b * c) ? = ab * ac
We are now going to use the Properties of Real Numbers to decide if the statement is true. The Associative Property of Multiplication tells us that the grouping of factors does not affect the product. Therefore, we can remove the parentheses. Next, we are going to simplify further.
Having simplified both sides, we see that the expressions are different since the exponents of a are different. Therefore, the expressions are not equivalent and the statement is false. To find a counterexample, we will substitute arbitrary values for a, b, and c. Let's use a= 2, b= 3, and c= 5.
Since 30≠60 we know that the given expressions are not equivalent. Finding just one counterexample is enough to show non-equivalence. In fact, these expressions will be equivalent only for a=1.
