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Exponential Expressions & The Order of Operations

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  • 0:07 Mathematical Equations
  • 0:42 Order of Operations
  • 1:41 Order of Operations Example
  • 3:46 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
When performing mathematical operations, there is a specific order in which the operations should be performed. This includes when to simplify the exponents. This lesson will describe in what order exponents should be solved as you are performing mathematical operations.

Socks Before Shoes

When you are getting dressed in the morning, you put your clothes on in a certain order. There are things that must be done before other things. You MUST put your socks on before your shoes. And you really should put your pants on before your shoes as well.

Mathematical equations should also be performed in a specific order. If there was not an order, different people would look at problems in different ways and come up with different answers for the same problem. It would be chaos. And one mathematician might not be able to recreate another's work, which would cause confusion. There must be an order that everyone follows.

Please Excuse My Dear Aunt Sally

Please excuse my dear Aunt Sally. No, my favorite aunt did not just burp in the middle of the lesson. This phrase is a mnemonic that can be used to remember the order of operations for an arithmetic equation. The order of operations is just like what it says; it's the order in which each operation should be performed. The first letter of each word in the phrase corresponds to the proper order of how the operations should be performed.

P - Parenthesis: Every operation in parenthesis should be performed first.

E - Exponent: All exponents should be calculated next.

M - Multiplication

D - Division: All multiplication and division should be done next, in order from left to right. Not all multiplication, then all division, but both of them as they appear from left to right.

A - Addition

S - Subtraction: Finally, all addition and subtraction should be done in order from left to right.

Now that we know the proper order to solving mathematical equations, let's do an example:

Solve (2 + 5) - 3^2 * 5 + (3 - 1) - 4.

Following the order of operations, the first step to solving this problem is P - parenthesis. That means we need to solve the portions of the problem that are inside the parentheses.

(2 + 5) = 7

(3 - 1) = 2

Then our equation looks like this:

7 - 3^2 * 5 + 2 - 4

The second step is E - Exponents; so we simplify any exponents.

3^2 = 9

Which then simplifies our equation to 7 - 9 * 5 + 2 - 4.

The next two steps, M and D - Multiplication and Division, are combined. This means that we solve all multiplication and division problems in order from left to right. In this problem, there is only one multiplication problem, 9 * 5 = 45. Now our problem looks like this: 7 - 45 + 2 - 4.

The final two steps, A and S - addition and subtraction, are also done together from left to right. We can now solve the problem:

7 - 45 = -38

-38 + 2 = -36

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