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# Comparing exponent expressions

In this math activity, we arrange three math expressions from smallest to largest. We evaluate the expressions: 2 cubed minus 2, 2 squared plus 3 to the power of 0, and 3 squared. We find their values to be 6, 5, and 9. The correct order is 5, 6, and 9.

## 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.)
• 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).
• 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?
• yes because sal did used the 1st method as said in intro to exponents
• If 3 to the power of 0 is 1, then why not 3x0?
• They are 2 different operations, that's like saying " If 1+1=2, then why is 1-1=0?"
• i keep thinking that 3 to the power of 0 is 3 but i know its not but keep forgeting that its 1 how is it 1?
• It is because exponents represent repeated multiplication. Anything to the power of 0 equals 1. This ultimately means that the value always ends up being divided the same amount of times it was multiplied. 3^0 means, after you multiply by 3 a specific number of times, you are going to have to divide by 3 the same number of times. So regardless of whether you get to multiply by 3 one time, two times, dozens of times, hundreds of times, thousands of times, trillions of times, or even so many times that we can not imagine, every multiple is instantly removed and the only factor that remains is 1.
• is 0^0= undefined? or just 0
• it is going to be 0 because 0 to the first power is 0 and to the 2nd power also 0
• 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?
• 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)
• still don't understand why any number to the power of 0 is equal to 1.
• because, if you have 3 as a base, and the exponent is 4 that would equal 81 and if you keep lowering the exponent, than you will see a pattern!
3-4 = 81
3-3 = 27
3-2 = 9
3-1 = 3
3-0 = 1 if you look closely than you can see that we are dividing by 3 each time the exponent goes down! that's the best I can do to explain, hope this helps :)
• anything to the power of 0 equal to 1?
• With the exception of 0^0 which is indeterminate
• 9(3), 6(1), 4(2)
• 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?
• 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.

## 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.