Yes, the placement of parentheses can affect the value of an expression even when only multiplication is used. This is because parentheses can change the grouping of factors, which can in turn change the order of operations.
The order of operations is a set of rules that dictate the order in which operations should be performed in an expression. When there are no parentheses, the order of operations is as follows:
Exponents
Multiplication and division (from left to right)
Addition and subtraction (from left to right)
However, when there are parentheses, the operations inside the parentheses are performed first. This means that the order of operations is not always followed strictly from left to right.
For example, consider the following expression:
3 * 2 * 4
According to the order of operations, this expression should be evaluated as follows:
3 * 2 = 6
6 * 4 = 24
However, if we add parentheses to the expression, we can change the value:
(3 * 2) * 4
In this case, the parentheses tell us to evaluate the expression inside the parentheses first. So, we have:
(3 * 2) = 6
6 * 4 = 24
Therefore, the value of the expression is different depending on the placement of the parentheses.
This is because the parentheses change the grouping of factors. In the first expression, the factors are grouped as (3)(2)(4). In the second expression, the factors are grouped as ((3)(2))(4). This change in grouping changes the order in which the operations are performed, which can in turn change the value of the expression.