 This video is part two of X1 of Properties. Alright. So a new property. Suppose we had two to the third and we had it squared. Well that would be two over three times two over three. And if we multiply that gives us four over nine. So look back, two squared is four and three squared is nine. So just like we had the product raised to a power, we can say that we have quotient raised to a power. We just distribute the power to everything top and bottom inside. So again we're going to distribute the exponents. So let's try. A squared is going to be cubed and over three and it's going to be cubed. So we have an answer of A squared cubed. We multiply one as a power raised to a power. So A to the sixth and three cubed happens to be 27. Alright. When you have a negative there's a couple of things you can think of. You could rewrite this as negative three. Get rid of that negative and just put it with one of your numbers. Or this is really negative one. So negative one cubed is going to be negative one times negative one, which is positive one times another negative one will be negative one. Because we took a negative times itself three times we ended up with a negative. And if we back earlier we had one I think where if I had negative one and I had it squared, well a negative times a negative is going to be a positive. So there was a rule that says when we have an odd exponent and we're dealing with a negative inside the parentheses then we know our answer is going to be negative. And if we're dealing with an even exponent like this two and we have a negative inside our parentheses, no matter what it is inside there if it's a negative then we know that we're going to end up with a positive. I do this one using our rule. So I'm going to think about the negative here and because it's an odd power that tells me that my answer is going to be negative. So my fraction is still going to have a negative in front of it. And then I'm going to have three that's going to be cubed and I'm going to have m that's going to be cubed. And on the bottom I'm going to have four that's going to be cubed and I'm going to have n that's going to be cubed. Three cubed is 27. m cubed is just going to be m cubed. Four cubed is 64. And n cubed is just going to be n cubed. And finally, everything inside gets raised to that power. So two to the fourth. My base of five gets raised to the fourth. My base of x cubed gets raised to the fourth. Every factor inside there gets raised to the fourth power. So two to the fourth is 16. Five to the fourth, so 625 down the bottom. And then x cubed raised to the fourth power. Remember that means that we're going to mall to apply our exponents. And that gives us x to the three times four or twelve. Alright, let's expand. Let's do some expanding here. Eight factors of y. Why did I take such big numbers? Four, five, six, seven, eight. And three factors of y on the bottom. And I want to simplify. Remember when you simplify, if you have a common factor top and bottom, that gives you one. So there's one, there's one, there's one. And I'm only left with one, two, three, four, five factors of y on the top. If you look at this, the eight's bigger, so I would expect my leftovers to be on the top. Let's try again. Six factors of a. Four, five, six factors of a. Over four factors of a. Common factor top and bottom. We have four of them. And I'm left with a squared. So what did we do? I started out with an eight and a three and ended up with five. I started out with six and four and ended up with two. So we could say that when you have the same base and you're dividing, you take your base and you subtract your exponents. And I want to put a little caveat here and say that you need to subtract top minus the bottom. Let's practice. This is b to the nine minus four. How hard is that? Nine minus four is five. This is two to the ten minus six. So two to the four. Now, when I have this, here's my same base dividing. But I also have these numbers that I also have to divide. Don't cheat your numbers. So negative eight divided by four is going to be negative two. And then my y's will be y to the six minus two. The final answer is negative two y to the four.