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

Nov 14, 2015

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

#### Explanation:

The order of operations is $P E M D A S$.
$P$ 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
$M D$ stands for multiplication and division. Do both of these in a left to right order, at the same time.
(Example: $4 \times 7 + 15 \div 3 = 28 + 15 \div 3 = 28 + 5 = 33$)
$A S$ stands for addition and subtraction, which are also both done from left to right simultaneously.

In your scenario, $4 {\left(9 - 6\right)}^{2}$, it may be tempting to try to do use the exponent. However, we can't do ${\left(9 - 6\right)}^{2}$ without first knowing what $\left(9 - 6\right)$ is. This is why parentheses are always computed first.
We know that $9 - 6$ is $3$, so we can rewrite your original term as $\textcolor{b l u e}{4 {\left(3\right)}^{2}}$.

Now, which do we do next—multiply or square? In $P E M D A S$, 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 $\textcolor{g r e e n}{4 \left(9\right)}$. It is obvious that all there is to do now is multiply, leaving a final, simplified answer of $\textcolor{red}{36}$.