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Comparing exponent expressions

Compare three expressions with exponents.

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  • duskpin tree style avatar for user Ellen Ko
    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.)
    (6 votes)
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  • blobby green style avatar for user chrome11fr
    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)
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  • hopper cool style avatar for user zeo
    is 0^0= undefined? or just 0
    (2 votes)
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  • blobby blue style avatar for user Dojo Cat
    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)
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  • blobby green style avatar for user Dylan Maines
    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)
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    • hopper cool style avatar for user Philip
      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)
  • blobby green style avatar for user jmhorne
    Can you do bigger exponents?
    (1 vote)
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  • leaf orange style avatar for user hyunjinsong5
    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)
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    • winston default style avatar for user Dorito
      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)
  • male robot hal style avatar for user Rawat, Pranjal
    I thought you couldn't add or subtract the exponents which have different bases.
    (2 votes)
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  • hopper happy style avatar for user Ian Wu ✅
    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)
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  • duskpin tree style avatar for user 𝕋𝕦𝕩𝕖𝕕𝕠 𝕊𝕒𝕞
    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)
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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.