Main content

## 6th grade

### Course: 6th grade > Unit 4

Lesson 5: More on order of operations- Order of operations examples: exponents
- Comparing exponent expressions
- Order of operations
- Order of operations example: fractions and exponents
- Order of operations with fractions and exponents
- Order of operations review
- Exponents and order of operations FAQ

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Comparing exponent expressions

Compare three expressions with exponents.

## Want to join the conversation?

- My main question is why is anything to the power of 0 equal to 1?(I watched the videos a lot but still don't understand.I even PAY ATTENTION.)(7 votes)
- I like to think of it this way. 2^0 can be answered as 1 multiplied by two, zero times. The number one is not being multiplied by anything, not even the number zero. So the answer is the number one (1).(3 votes)

- is 0^0= undefined? or just 0(4 votes)
- it is going to be 0 because 0 to the first power is 0 and to the 2nd power also 0(2 votes)

- Sal:Here we have 3 to the 0th power, which is clearly equal to 1.

Me, thinking that anything to the 0th power is 0: ...Clearly?(2 votes)- yes because sal did used the 1st method as said in intro to exponents(4 votes)

- Hi, I am a little confused. So in this video, it says anything to the zeroth power is one. But in an exponents exercise, it says that it equals zero. I am so confused.

Sincerely

Candlelight(4 votes)- The reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity. There is a bug in the exercises, so give yourself a figurative mark.(1 vote)

- A Whole New World

If I could go anywhere for vacation, I would go to a whole new world similar to Earth, but untouched by humans. A place with no pollution, and a clear night sky. A new world is an exciting and mysterious place full of adventure.

I can imagine me walking into a beautiful clearing. There are unknown flowers that smell just like the ocean! The Grass sways side to side like two lovers dancing at a ball.

Sunlight shines through the leaves and branches, leaving small, light dots on the ground. The grass is soft, like a fluffy pillow. When it’s night, I can look up and see all the stars. They are so beautiful! The sky isn’t just black with a few white dots here and there. There are brilliant shades of green, blue, purple and red. All ranging from almost black to nearly white. And the stars, there are so many! Too many to count. I could gaze upon them for forever as they twinkle and wink at me from space.

When I climb up to the treehouse I made, I can see everything the eye can see, because it’s the highest tree the world has ever seen. During the summer the air is warm, and the breeze tickles my face. During the winter, when the breeze gets too strong, and my hair freezes to my head, I can curl under my soft fur blankets and listen to the soft creaking of the branches as my tree rocks me to sleep. And when I’m hungry, I collect all sorts of nuts and berries that taste amazing!

At the bottom of my tree there is a small babbling brooke. I can see tiny fish and tadpoles swimming around the shallow ends. It’s not really a good source of food, but it is very pretty to look at. The water is always crystal clear and ice cold. Sometimes, I occasionally see a deer or two drinking from this brooke, and when it sees me it would bound off into the woods. When the wind blows, it’s almost like the trees are moving in welcome. Welcoming to their home.

When I’m not gathering food, I’m out exploring. I found a really cool meadow, and I love to lay down and smell all the flowers. Lavenders dance in the wind, and bees buzz around collecting pollen and drinking sweet nectar. Being in a new world would be amazing, think about it.

What do you guys think?(3 votes) - I am not understanding the logic of 3 to the zero power = 1.

The way my brain works is taking 3 and multiplying it by itself 0 times, which would equal 3. Where do we get 1 from? Is it just a rule that we should know when to apply?(2 votes)- Anything to the power of zero (except 0) will equal 1 because exponents are repeated multiplication, and a power of 0 means the value was multiplied by itself 0 times. Since anything times 1 equals itself, after we "factor out all the multiples" the final value we will be left with is a 1.(2 votes)

- Can you do bigger exponents?(1 vote)
- Yes, the exponent can be as large as you want.(4 votes)

- Hi,

On a different video, Sal says that 0 raised to the power of 0 is left*undefined*. In this video, he says it equals 1. Did he just pick it? Was it specified in the question?(0 votes)- It depends on who you talk to. Some people say that 0^0 is 1, some people say it’s 0, and some people say it’s undefined. The most common thing I’ve heard people say is that 0^0 is 1. If you put this into a calculator, then it will say 1. (I know Google and the Khan Academy calculators say this)(6 votes)

- I thought you couldn't add or subtract the exponents which have different bases.(2 votes)
- How do you solve 1^-1, 1^-2, 1^-3, 5^-1, 5^-2, 5^-3?

Thank you so much if anyone could help out!

Thanks to Khan Academy for this awesome explanation video and for whoever that answers my question!(2 votes)

## Video transcript

- [Instructor] So we are asked to order the expressions from least to greatest and this is from the
exercises on Khan Academy and if we're doing it on Kahn Academy, we would drag these little tiles around from least to greatest, least on the left, greatest on the right. I can't drag it around 'cause this is just a picture, so
I'm gonna evaluate each of these, and then I'm gonna rewrite them from least to greatest. So let's start with two to the third minus two to the first. What is that going to be? Two to the third minus two to the first. And if you feel really confident, just pause this video and try to figure out the whole thing. Order them from least to greatest. Well two to the third, that
is two times two times two, and then two to the first,
well that's just two. So two times two is
four, times two is eight, minus two, this is going
to be equal to six. So this expression right over here could be evaluated as being equal to six. Now, what about this right over here? What is this equal to? Well let's see, we have two squared plus three to the zero. Two squared is two times two and anything to the zero power is
going to be equal to one. It's an interesting thing to think about what zero to the zeroth power should be but that'll be a
topic for another video. But here we have three
to the zeroth power, which is clearly equal to one. And so we have two times two plus one. This is four plus one,
which is equal to five. So the second tile is equal to five. And then three squared,
well three squared, that's just three times three. Three times three is equal to nine. So if I were to order them from least to greatest, the smallest of these is two squared plus three
to the zeroth power. That one is equal to five,
so I'd put that on the left. Then we have this thing that's equal to six, two to the third power
minus two to the first power. And then the largest value
here is three squared. So we would put that tile, three squared. We will put that tile on
the right, and we're done.