How do you simplify #4(9-6)^2# using order of operations?

1 Answer
Nov 14, 2015

Answer:

Simplify the terms in the parentheses, then raise to the exponent, then multiply.

Explanation:

The order of operations is #PEMDAS#.
#P# stands for parentheses—you should always try to make whatever is inside the parentheses as simple as possible.
#E# is for exponent—raise numbers to exponents as soon as parentheses are as simple as possible
#MD# stands for multiplication and division. Do both of these in a left to right order, at the same time.
(Example: #4xx7+15-:3=28+15-:3=28+5=33#)
#AS# stands for addition and subtraction, which are also both done from left to right simultaneously.

In your scenario, #4(9-6)^2#, it may be tempting to try to do use the exponent. However, we can't do #(9-6)^2# without first knowing what #(9-6)# is. This is why parentheses are always computed first.
We know that #9-6# is #3#, so we can rewrite your original term as #color(blue)(4(3)^2)#.

Now, which do we do next—multiply or square? In #PEMDAS#, exponent comes before multiplication, so we will square the #3# before we multiply by #4#. Doing this in reverse is a very common mistake!

Once we square the #3#, we get #color(green)(4(9))#. It is obvious that all there is to do now is multiply, leaving a final, simplified answer of #color(red)(36)#.