Okay, we're going to talk about roots and reciprocals. of literal numbers. And as I say here in the first bullet, our root can also be found, by literal numbers, the procedure is the same as with decimal numbers. So I give you an example I say okay, find the fourth root of A to the eighth. And again, is my graphical representation. So all I do is I divide the exponents by the root.

So in this case, eight divided by four, that equals two. And so my answer is A to the two. So when I want to find the fourth root of A to the eighth, it is Have a squared. Okay? And when I look at reciprocals here, okay, one over a squared equals equals A to the minus two and one over eight of the minus two is a squared. So that's pretty much it.

If you look at it, it's the same as we had a decimal number. Again, what is a literal number? It's a letter that replaces a value of a decimal number. All right, down here, I give you some examples. We want to find the indicated root. I want to find the cube root of eight B to the third power.

And again, all I do is break it up. So I find the cube root of eight and the cube root of b to the three What do I have? I've got two times B, because the cube root of eight is two. And again, when I'm looking when I have a literal number, and that literal number has an exponent, I want to find the, the, the cube root in this example of that I just divide. So what would over here, all I do is divide that exponent, so what would it be three divided by three equals one. So that would be B to the one raised to the One Power.

I really don't need the one there. So I get rid of that. So my answer is to be right there. All right. Um, let's clear the slide and I'll expand upon the last example here for you. Last example right here.

Okay, why do the eighth to the half power? Well, we know when we have a half power that in this example are always it's the square root. So I'm going to rewrite that right there. So y to the eighth, I'm looking for the square root of y to the eighth. Again, when I have a square root, it's two. So all I do is divide eight by two, that equals four.

So my answer is y to the four right here. Why race to the fourth power? All right, let's clear the slide. And let's go on to the next slide. And here, I give you some examples. I'd like you to do them.

All right. See if you can do them. This one here. If you remember, I'm just going to start it not finish it. So what are we looking for? We're looking for eight cubed times I, and now you know what to do, you need to find the cube root of eight.

Unite need to find the cube root of b to the three. What do I do? In this one here? I divide the exponents. All right, okay answers on the next slide. Stop it do them.

You'll see the answers on the next slide. All right, well, here you go. Here are the answers. I could call them off and you can you can see them there. Again, if you have any problems go over the material. It's it go over it.

It's not that difficult. You should be able to get these if You followed along with me through this course. So if you still do, then send me an email, give me a call. But we're good. So we're going to go on to the next topic. All right, on this slide here, we're going to talk about evaluating the equations.

And if you notice, I assign a number to the literal number. And in this example, a will equal to b will equal three. And we've got these equations here, and we're going to substitute them now I'm going to do one or two of them for you. And I think possibly we'll do we're going to start with this one. And we're going to do this one here. All right.

So let's, let's do them. Alright, so we're going to do to be squared I mean All right, and we know from previously, what is it a equals two and B equals three. All right, so let's just do it this way, too. And this does many ways. I'm going to do it this way. Okay?

Times three. And that's going to be all squared. So if you remember I do what's in the parentheses first. Right? Now I need to square that. Six times sixes.

So my answer is 36. Okay. All right. Let's stop. there and let you look at that. And we'll do the next one.

All right, the next one I'm going to do for you is this one here are the square root of 16 A squared. So let me let me white out the screen and I'll show you how to do it. All right, here it is. We're looking for the square root of 16, eight to the sixth. And remember, even though we don't show it in square roots, there's assumed that a twos there. All right, so I can do this.

Now I can break that 16 and say the square root is 16 times a square root of eight to the six. All right, so let's find the square root of a eight of the square root of 16. The square root of 16 is the four is four. Now what do I do with this one remember, my ex bonuses divide. So what do I do? I divide six divided by two equals three.

So I have four a cubed equals four. And that means multiplication, a equals to two cubed. Okay? And that's eight. All right, so I got four times two cubes, so that's two times two times two. Two times two is four times two is eight.

Now four times eight is What? 32? So my answer here is 32. All right, all right, let's go back. Okay, well, here are the answers. Really, if you, if you're just looking at them, that's fine, but at least make an attempt to try them.

Try them. That's the only way you're going to learn is you're going to have to try them. And when you do a couple and you get the hang of it, they're they're not that bad. All right, we're going to go on to the next topic now and again, you know how to get ahold of me if you need some help.