Okay, in this section here, we're going to talk about powers and roots. We're going to talk about positive exponents, roots of positive numbers, square and square roots, powers of negative numbers, powers and roots of fractions, and square and roots with terms. So let's just go on and go to the next slide here. Okay, they this may be a little bit of a review here, but we're talking about positive exponents and positive exponents, provide a shortcut method of indicating repeat multiplication of the same number. Right there. All righty.

And I give you some examples. For instance, we have two to the third here. Well basically all that is is We multiply to three times two times two is four, that's the power of two plus two again is eight. So two cube, which is two times two times two, and the answer is eight, or four to the third, again, four times four times four. Well, one times four is four, and four times four is 16. Four times 16 is 64.

So basically, we're just taking the, the root and multiplying it by the number of times that determined by the by the exponent or the positive exponent here, right here, and right there. All right. And my recommendation to you is, we should use a calculator for this because it can get monotonous I for instance, I give you an example here. 16 cube will We know we're going to multiply 16 by itself three times. So I recommend in this using the, the calculator that comes with the operating system here, I've got windows. So I'm going to pull that calculator down and do these two examples for you.

You can use a standard calculator. There's probably some calculators on the internet that you can search for news. So I'm going to stop here and get my cat my calculator down. And we'll do these two examples. Okay, we're going to do the first example here. 16 to the third power.

So I've got my calculator out here. So all I do is make sure that I'm in scientific mode here because I don't believe we can go to regular standard on here. Yeah, you got to be in scientific mode. Right there. Alright, so make sure it's a scientific. So let's do this 116.

So I plug in the number 16. If I look at this function here, this has given me the value of x. See it says x to the Y. Well, this is giving me the value of x. Now notice the little carrot pointing up right there. That's where we want to put the three.

So we do three, and we hit equal, so it's 4000 096. All right, so that's my answer there. Alright, let me see if my pen works. And I'll put it on there. All right, so we got 4000 096. All right, let's do the next 112 to the fourth power.

Let me bring my calculator down. And I'm going to move it up, I'm going to clear it. And again, I'm going to plug in 12. I'm going to use this function here. Again, make sure you're in scientific mode. And now I'm going to put the four and hit equals.

So what's 20,000 763? That's my answer. That's it. So I suggest that you use the calculator. When you do these API, there's no there's no need. We know that 12 to the fourth, we're multiplying 12 times 12 times 12 times 12.

You understand that? All right. Just make sure that when you're plugging the numbers into your calculator, use, you spend a lot of attention making sure that you put in the right numbers because it's very easy to make mistake. All right, let's stop here and go to the next slide. All right, on this slide here, we're going to talk about roots, the roots of positive numbers. And the root is the value that we can multiply it by itself to equal the original number.

So for instance, I give you an example, the cube root of 125. Okay, well, let's five because if I multiply five, times five, times five, that'll equal 125. So it's the number multiplied by the root here or the exponent, that will give me the number in the radical sign because if you read Remember, that's called a radical sign. All right. So I suggest you use a calculator. Now if you look at the calculator that we brought down in the previous slide, it doesn't, it does not have that function.

So there's one online. I mean, there's a lot but there's one online here that you can use. And I'm going to bring that up for you right now. Let me just move it in here. And basically, let me just bring this down. So for instance, right here is where I put my power.

So I'm going to put three and then if you notice, there's my radical I'm going to put my 125 in there. All right, and then I'm going to say calculate, and the answer is five, like I showed you right here. So the cube root of 125 is five, which means if I multiply go back the opposite way, if I multiply five times five times five, I'll get 125. All right. All right. So let's, um, let's clear this.

Gonna minimize that for a minute. And another example that I give you, is 16. What's the how many, okay? What number multiplied by itself, four times will give me 16. And if we bring out the calculator Go back here I switch programs, whoops, switch, switch programs. Here we go.

Whoops, that's not the one I want. Sorry about that. Let's go to this one. Okay, so let's do four, we'll put my four in there. And then we're going to put 16. And then we're going to calculate that.

And notice it's plus a minus two. So what does that mean? Well, if we have an even number of minus signs, the answer is positive. If we have an odd number of minus signs, the answer is negative. So since we have two times two times two times two, which is even, we get 16 If we go minus two times minus two, which is a plus four minus two, which is a minus eight times a minus two, minus eight times a minus two is plus 16. So that's why when you plug that in, we get a plus a minus 16.

Because we have an even number of minus signs. Okay? So let's just bring that back. All right, let's use the calculator. For example, skier, this one here. So let me get my calculator down.

Change the pointer to an owl. There we go. And let me just reset that. So I'm going to do four Put the four in there. And I'm going to do 2407. And I'm going to calculate it and 2401.

I'm sorry, go back. Let's recalculate that. plus a minus seven. All right, we talked about that, because we must have a even number of negative signs and we do see the four. That four tells me it's even right there. All right.

So seven, may it be plus or minus, multiplied by itself four times will give me 2401. Right there. All right, let's reset this and let's do the bottom one. So now we want to put the three in there and we want to put the one seven to eight. We want to hit the calculate, and we get 12. So 12 multiply it by itself three times will give me 1728.

That's it. Use the calculator on the next slide, we're going to give you some couple of problems to do do them with the calculator. If you follow this, that should be pretty much straightforward. Okay, before we go on I, I remembered I need to mention this. We've been talking about this here. That's how we define routes.

So for instance, if I show you down here, I'm looking for the cube root of eight. Okay, I've got my radical sign. We know right here that we're looking for the cube root but we can also show it this way. Right here, where y is the number that we're looking to find the root of. And we have one over x, where x up here is the number we want the number of the route we want to find. For instance, it would be three, right here.

All right? That's it. It's just a different way of showing it. The way I manipulate it, or the way I find the answer is basically the knot basically is the same. And that's it. And I show you just one more example here.

Okay. 16 and we're looking for a number that multiplied by itself four times will give me 16 right here, and here's my 16 and There's that one over four. Okay? And again, I manipulate it the exact same way I take my calculator, and I'll go in and I'll do this same exact thing. Alrighty. So I just wanted to show you this.

It's just another way of presenting it. Nothing's changed other than a way, or presenting how we do this. Okay, here, here's some examples. Use the calculator on the iOS for these and use the one that I found on the internet, which is a very nice calculator for these here. Take a few minutes, do them and then when you continue, you'll see the answers on the next slide. Okay, here are the answers.

You can look at them. I've been repeating the answers in the previous but put the slides right there. I'll leave the slide on for a few minutes. Take a look at them. At the beginning of this section and at the end of the section, you'll see a help number. Give me a call.

I'll also put a worksheet up on this platform with a few more exercises you can do. Okay, we're going off