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## 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

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# Comparing exponent expressions

Compare three expressions with exponents.

## Want to join the conversation?

- 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(3 votes)

- is 0^0= undefined? or just 0(2 votes)
- it is going to be 0 because 0 to the first power is 0 and to the 2nd power also 0(2 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(3 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)

- 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)
- 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.)(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) - Zero to zeroth power is often said to be "an indeterminate form", because it could have several different values. Since x0 is 1 for all numbers x other than 0, it would be logical to define that 00 = 1.(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.