Multiplying and dividing literal numbers with exponents is what we're going to talk about here. So we write here the first bullet, okay, multiply the numerical coefficient of the literal base to obtain the new coefficient, add the exponents. The base must be the same. Let's see what we mean by that. Okay, so for an example here, I say, Okay, let's multiply six A squared by three a Q. All right, so what's that kind of equal?

There it is right there. Well, we multiply the coefficients and we you know from, from our previous discussions, there are my coefficients right here. So six times three is 18. Okay, since the base of the exponent saw the same for both terms. term term, the exponents are added to plus three. So here we go.

18 A to the fifth. That's my answer. Okay, um, I don't think we need to go into that any deeper. But what I would like you to do is, take a few minutes, stop the presentation, and just do these and again, the answers are on the next slide. Alright, see over there. Okay, here are the answers for you.

Or they are right there. I'm not going to call them out. You can. You can read them. They should be pretty, pretty self explanatory. Again, all we do, and I'm going to pick one here, multiply the coefficients, so I got two times three there.

They're equal sex. And all I did do is add the exponents. In this case, five plus four equal nine. So my answer is C six A to the nine, because my bass is the same, the A's. Okay? All right, that's it.

See on the next one. Okay, we're going to talk about dividing literal numbers with exponents on the slide here. And if we look at some of the rules, divide the numerical coefficients of the literal base to have to obtain the new coefficient. So when we multiply we multiply the coefficients when we divide. We Divide the coefficients, all right, then we subtract the exponents, the base must be the same, just like in multiplication, we added the component of the exponents. The base had to be the same, but when we divide, we subtract them.

All right, so let's look at this example here. Eight a cubed by two a. And this is how we write it. A cube divided by two a, and then we've got eight, a cubed over two A. So the first thing we want to do is we want to break that out and we want to divide the coefficients, eight divided by two, and we know that equals four. And since the base of the exponents are the same, meaning they're both as the experts ponents are subtracted.

So we've got three and this is assumed to be one even though we don't show it. three minus one equals two. So therefore, my answer is four A squared. Because here's my coefficients, and I subtract my exponents, as we show here. And there we go. Alright, so there's my answer.

All right, so you should have a good handle on this. Here's some problems for you to do. And I suggest that you do hit the pause button, and you do do them. And again, the answers will be on the next slide. All right, this will help you to understand what we just went over. Okay.

All right. Um, I'm not going to go over gnome or yellow. The wall I should say give you the answer. There right there. Again, if you have any questions, you have a number. You have a way to contact me via this platform.

And listen, see, I will give you a call. All righty. With that said, we're going to go on to the next subject. Okay, and this slide here we're going to talk about fractions with literal numbers. And in lead Gan, let's look at the bullet points here. The first bullet point, literal numbers represent entire quantities, that could be part of a fraction.

All right. Let's see what that means. Let's go on to the second one though. literal numbers can be in the numerator or don't nominator. So I show you some examples. All right, we have a over two here.

And the literal number is in the numerator. Over here, I have two x divided by three. And the literal number is also in the numerator. This last one, a plus b over C. We have literal numbers that are both in the numerator and the denominator. Okay. Let's look at the last bullet here.

Fractions containing literal numbers can be added, subtracted, multiplied and divided just as decimal numbers Okay, so we treat the literal numbers as desk small numbers and look, let's look at some of the examples that that I've given you here. All right, right here, I say add two over a, and three over a. So basically, that's what we have. That's our equation. We know that the denominator can be combined because it's the same the literal numbers a and it's the same. So all we do is add the numerators two plus three, and here's my answer, five over a in multiplication.

Let's see what happens here. So we want to multiply to a by three A, which I show you here. So all we do is multiply the numerators and the denominators, so two times three is six. And we know that a time A is a squared. So my number is six over a squared right there. Again, we want to divide to a by three, which I'm showing you here.

And what do I want to do? I want to take the reciprocal. So if you remember, I flipped this. So this becomes so three over a, b becomes B over three. And so I just multiply two times B is two B. A times three is three a.

And here's my answer right there. Okay. Last one, find the cube of A over two. Well, we just take a over to and we we find the third power and if you remember We, we can just break this up. And so we have a over three. And I'm sorry, a cubed, and then two cubed.

So a three stays is a three, and the two times two times two or two to the third power is eight. So I've got a, a cubed over eight, and there's my answer there. Right here, I want to subtract two a from three a. So again, it's it's almost the same thing as addition that we did over here. But instead of adding the numerators, I subtract them. As you can see, a stays the same.

So I have three minus two over a, and the answer is one over a. And now I'm going to find the cube root this example here. Finding the cube root of a cubed over eight. It's the same as a cubed over eight. We're in the cube root bracket. And I break that up cube root of a cubed in the numerator.

And we're looking for the cube root of eight in the denominator right here. So I just pulled them out one at a time, a cubed. If I'm looking for the third root of a cube, what do I do? I divide the exponents. So three over three is one. There it is there.

And what's the cube root of eight? It's two. So my answer is a over two. Okay, let's clear the slide. And let's go to the next one. All right on this slide here.

I give you some problems that I'd like you to do. But I think I'm going to do what I'm going to do like one or two of them for you. Just to kind of reinforce this. So I've picked two here. Let's see. Why don't we do this one?

And let's see, why don't we do this one. So we'll do what? We'll do this one here first. Alright, so I'm going to wait out the screen. And we're going to do them. So let me let me wipe the screen out.

Okay, so here's, here's the first one to a plus one, over two plus to a minus one. Over four, well, we want to add them What is one of the things that we want to do here, we want to make sure that our denominators are the same. So by looking at that, I can see that if I multiply here by two, I will get my denominator the same. So I'm going to multiply my opes my denominator by two, and my numerator by two. So two times two, a is four a, and two times one is two. Two times two is four.

Now I have a common denominator. So I have for a plus two plus to a minus one. So now all I do is add my terms. So four a plus two A is six a plus two minus, plus a minus one, two plus a minus one is a plus one over For, and that's my answer. All right, on the next one here, we're doing a over two times a B over four, and we're going to multiply them. Okay?

So all I do is multiply these two factors A times A is a squared, a times V is be. Okay. Then we multiply the denominators which is eight. So here's my answer a squared b over eight. All right, a squared b over eight. All righty, All right, well, we'll back out here to this slide.

So what, again, take a few minutes, or as long as you need, stop the presentation and do the rest of the problems. And as always, the answers will be on the next slide. But again, I've preached this and preach this take the time and do them. Alright, with that said, we'll see you on the next slide with the answers. All right, here are the answers as I've promised, take a look at them. If you have any questions, again, you know how to send me an email through this platform.

At the beginning of each presentation, there is a phone number you can call it, I may or may not be there. I do not respond to block numbers and unfortunately, I cannot return international calls. So We'll help you out. If, if you can't get ahold of me that way again, send me an email or or through this platform communicate with me. I'll work it out with you. All right, we're done.

This concludes this lecture. The next lecture will be with factors and terms. So we'll see you over there. Take care