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### Course: 6th grade (Eureka Math/EngageNY) > Unit 4

Lesson 1: Topic B: Special notations of operations- Intro to exponents
- Squaring numbers
- Intro to exponents
- Meaning of exponents
- Powers of whole numbers
- The zeroth power
- Exponents of decimals
- Powers of fractions
- Powers of fractions & decimals
- Exponents review
- Order of operations introduction
- Order of operations examples: exponents
- Comparing exponent expressions
- Order of operations (no exponents)
- Order of operations
- Worked example: Order of operations (PEMDAS)
- Order of operations with fractions and exponents

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# Order of operations examples: exponents

The order of operations (PEMDAS) is essential for solving math expressions correctly. By following Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction, you ensure accurate results. Understanding the impact of parentheses on calculations helps avoid common mistakes and enhances problem-solving skills. Created by Sal Khan.

## Want to join the conversation?

- I have a question. At3:33, Sal says we have multiplication and division. He proceeds to do the division first. 81 / 9 = 9. Shouldn't you do the multiplication first? 5 * 81/9? Working left to right? Because there are no Parentheses and there are no exponents. In the first video "Intro to order of operations" Sal states that you should work left to right when mult./div. and add/sub.?(55 votes)
- With PEMDAS multiplication and division are of equal importance in order of operations. If you multiply by the fraction 81/9 you would get the same answer. The reason Sal divided first was because it made the problem easier to solve, because 5 times 9 is easier than 5 times 81/9. If you don't believe me try it on your calculator and you will get the same answer either way.(29 votes)

- Having trouble trying to solve this

7+8(15-9) exponent of 2(16 votes)- 7+8(15-9) with the exponent of 2 right? first follow BEDMAS/PEMDAS or whatever order of operations you use, first comes brackets/ parentheses so you solve 15-9 which is 6 so it should be 7+8*6 with still the exponent of 2 oh and btw its multiplication because if there is no operation there and there is a bracket beside the number that is basically the multiplication sign! anyways moving on exponent goes next so since 6 with the exponent of 2 is 36, you should write 7+8*36 then you simple multiply 8 * 36 that gets you 288 so 7+ 288 will equal to 295. hopefully that helped you if not srry im not that good at explaining things XD but the answer should be 295 :)(11 votes)

- I made up this one Please Eat My Delicious Artichoke Soup(16 votes)
- Would like more examples like these(16 votes)
- You can call this Please Escape My Dead Anaconda Snake, this is a very funny way. Its my favorite one.(19 votes)
- you mean play escape the dyinng anaconda snake(1 vote)

- I always find it easier to remember PEDMAS as an acronym. I learned "Please Excuse My Dear Aunt Sally." I thought everyone learned it this way but I guess not. I hope it helps!! :)(6 votes)
- Indeed!

In addition to this I'd like to break down what is the meaning of the acronym,**PEMDAS**for those who may be confused.

P for**Parenthesis**

E for**Exponents**

M for**Multiplication**

D for**Division**

A for**Addition**

S for**Subtraction**(10 votes)

- Does a negative plus a negative equal a positive?

I think I know the answer, I just need a refresher.(7 votes)- No. Say you are 4 dollars in debt, but then suddenly you go for more dollars into debt. Then you would not have no debt-instead you would be in 8 dollars of debt. If you are doing multiplication, however, then yes, they would turn into a positive.(3 votes)

- I didin't learn about exponents yet so that makes doing the exercises much difficult does anyone where i could learn that(5 votes)
- I have a question you see the 1+5*81/9,what do we do with the 81?(5 votes)
- so we do the multiplication and division since there are no exponents or parentheses. in this case we can do the division first even though we should work left to right and that makes the problem
*a lot*easier to solve. so it would be 81/9=9 then times the five plus the one. or in other words: 81/9=9*5+1(1 vote)

- why is the distributive property not used for the ones with exponents and parenthesis?(5 votes)
- Because you'd get the wrong answer then. You use the distributive property when you have a number to multiply inside the parentheses, not an exponent.(0 votes)

## Video transcript

So I have six
different expressions here, and what I want you
to do is pause this video and try to calculate the value
of each of these expressions. I'm assuming you've
given a go at it. Now let's work through them. So when we see
something like this, we have to remember our
order of operations. We have 2 times
3 squared, and we have to remember that the
first thing we would need to think about are
the parentheses. I'll just write paren for short. Then we worry about exponents. Then we will worry about
multiplication and division, and actually let me
write it this way. We worry about
multiplication and division. And then we worry about
addition and subtraction. So in this expression
right over here, there are no parentheses, so
we do the exponents first. So we calculate
what 3 squared is. 3 times 3 is 9, so
this becomes 2 times 9, which is equal to 18. Now let's look at this one,
and this one is interesting, because they have-- it looks
like the same expression, but now there are parentheses. And because of
these parentheses, we're going to do
the multiplication before we take the exponent. So 2 times 3 is going
to be 6, and we're going to take that
to the second power. So that's 6 times 6,
which is equal to 36. Now let's think about
this one right over here. Once again, we want to do our
multiplication and our division first. So we have a division
right over here. 81/9 is the same thing
as 81 divided by 9, and that's going to be 9. And then we have-- so it
becomes 1 plus 5 times 9. Now we want to do the
multiplication before we do the addition, so
we're going to do our 5 times 9, which is 45. So this becomes 1 plus 45,
which of course is equal to 46. Now let's tackle this
one right over here. So, we would want to
do the exponents first. So, 1 squared, well
that's just going-- let me do this in
a different color. 1 squared is just
going to be equal to 1, so that's just going
to be equal to 1. And so you have
2 times 4 plus 1. What should you do? Should you add first or do
the multiplication first? Well multiplication takes
precedence over addition, so you're going to do
the 2 times 4 first. 2 times 4 is 8, so
you're going to have 8 plus 1, which of
course is equal to 9. Now you have a very
similar expression, but you have parentheses. So that's going to force you
to do what's in the parentheses before you take the exponent. But within the parentheses
we have multiplication and addition, and
we have to remember that we do the
multiplication first. So we're going to
do the 2 times 4 first, so that's going to be
8 plus 1 to the second power. 8 plus 1 is 9, so that's
9 to the second power. 9 squared is the same thing as
9 times 9, which is equal to 81. Now we have one
more right over here that looks very
similar to this one, except, once again, we
have parentheses that's making us do the addition first. Without parentheses, we
would do the multiplication and the division first. But here, we see
that 1 plus 5 is 6, and then we have this
81/9, which is 9. So this simplifies to 6 times 9,
which of course is equal to 54.