Comparing exponent expressions

- [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.