Comparing exponent expressions

So we are asked to order the expressions from least to greatest. This is from the exercises on Khan Academy. If we're doing it on Khan 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 because this is just a picture.

I'm going to evaluate each of these and then I'm going to rewrite them from least to greatest. So let's start with (2) to the third minus (2) to the first. What is that going to be? (2) to the third minus (2) to the first. If you feel really confident, just pause this video and try to figure out the whole thing—order them from least to greatest.

Well, (2) to the third, that is (2) times (2) times (2), and then (2) to the first, well that's just (2). So (2) times (2) is (4), times (2) is (8). Minus (2), this is going to be equal to (6). So this expression right over here could be evaluated as being equal to (6).

Now what about this right over here? What is this equal to? Well, let's see. We have (2) squared plus (3) to the (0). (2) squared is (2) times (2), and anything to the (0) power is going to be equal to (1).

It's an interesting thing to think about what zero to the zero power should be, but that'll be a topic for another video. Here we have (3) to the zero power, which is clearly equal to (1). So we have (2) times (2) plus (1). This is (4) plus (1), which is equal to (5).

So the second tile is equal to (5). And then (3) squared. Well, (3) squared, that's just (3) times (3). (3) times (3) is equal to (9).

So if I were to order them from least to greatest, the smallest of these is (2) squared plus (3) to the (0) power. That one is equal to (5), so I'll put that on the left. Then we have this thing that's equal to (6), (2) to the third power minus (2) to the first power. And then the largest value here is (3) squared. So we would put that tile, (3) squared, we will put that tile on the right, and we're done.