The associative property for multiplication states that:
$(A \times B) \times C = A \times (B \times C)$
What happens in the case where there is an expression with more than $3$ factors?
For example, $(A \times B) \times C \times D$, since the associative property for multiplication only gives us a 'rule' for $3$ factors.
Would it be accurate to define a number, $E = C D$
and then if :
$(A \times B) \times C \times D$
$= (A \times B ) \times E$
$= A \times ( B \times E)$
$= A \times (B \times (C \times D) )$
$= A \times (B \times C) \times D$
which would show that the order of multiplication of any of those factors doesn't matter.
Can you use this logic for a larger amount of factors to conclude that rearranging the parenthesis in a multiplication won't change the result?