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Robert McKeown: Here we have a question asking

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us about exponents. So let's take a look at the

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left question first. And it's pretty

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straightforward. What does four to the power of

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two mean? Well, that just means it's four times

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four divided by negative three, which is equal

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to 16 over negative three, which is equal to

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negative 16. Over three. If the negative and the

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nominator are numerator, it doesn't matter. The

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whole fraction is negative. Now let's take a

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look at our right hand side question. So what

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does the exponent mean here? Well, a couple

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things. Notice that the negative sine is outside

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the exponents. So this is like writing negative

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one, multiplied by five over four to the power

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of three. And that's like writing negative one,

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multiplied by five over four times five over

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four times five over four. I could rewrite this

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in another way, I could say, Oh, well, this is

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like negative one, multiplied by five to the

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power of three divided by four, to the power of

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three. Right? So they all mean, the same thing.

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What's the answer going to be? It's negative

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one, or negative. Five times five is 25 times

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five is 125. Four times four is 16, times four,

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that's 64. And, you know, basically have

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negative 125. Over 64. Here we are on ALEKS. And

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we have the same question that we saw in my

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slides. And so we evaluated the exponents. And

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then we wrote it as fractions. So the first one,

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the answer was negative 16. Over three. And the

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second question was negative 125? over 64? Let's

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see if we've got the right answer. And we do. We

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will look at some more difficult exponent

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questions in the later topics. But for now, this

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is the basics. Our last question, I'm going to

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let you answer. And so if you look at the slide

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in front of me, the question says, if we divide

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a real number by zero, so that's something like

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five divided by zero, or two divided by zero or

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three, divided by zero? What happens? Can we do

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this? And if we can do this, can't? What's the

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answer? And so this is a multiple choice type

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question. And so the first option is if we

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divide a real number by zero, there is no

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problem. Mathematicians frequently divide by

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zero. The next option is that the universe will

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cease to exist. So that would cause some sort of

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reverse Big Bang. And that would be the the end

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of the universe as we know it. The answer any

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number divided by zero is always equal to

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infinity. And our last option is, if we divide a

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real number by zero, the answer is unknown.

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If you want to keep thinking about it, why don't

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you hit pause? And then I'll walk you through

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the solution. So is a the correct answer. Well,

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no, a is not the correct answer. There is a

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problem and mathematicians do not frequently

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divide by zero. Well, the universe cease to

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exist. Well, no, that's not a very good answer.

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You know, if we write down five divided by zero,

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the universe doesn't come to an end. The answer

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is always infinity. This is a tempting solution.

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However, infinity is not a number. So it is not

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an appropriate solution. infinity is a concept,

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not a number. If we divide a real number by

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zero, the answer is unknown. We do not know what

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the answer is, essentially, we don't know. So if

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you're going to divide any number by zero,

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mathematician say, we don't know what the answer

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to that is. And so you can never do it. Because

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if you do it, we won't have an answer for you.

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We do not know that some real number divided by

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zero produces infinity. We don't know what it

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produces. So why am I asking you this question?

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Because as we'll see, and some of the future

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questions and future topics that come up, you

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must never divide by zero. If you must divide by

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zero to get an answer, then we say that there is

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no solution. There is no solution. So this is

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going to come up in some future topics. You

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might wonder why and I'm trying to fill that in

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for you right here. We don't know what a real

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number divided by zero is equal to. So that does

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it for topic one, I hope you found it helpful.

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Remember, there are still a lot of concepts in

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topic one in the real number line that I didn't

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cover. And I think you're better off trying to

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learn those on your own. And if you have any

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questions, by all means, reach out to me, or

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take advantage of any other resources that are

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currently available. I would certainly be glad

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to help you. Now let me show you how to review

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this topic and how to get more assistance on

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this topic in ALEKS. So here I am on ALEKS. I've

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got an account that I've created where a certain

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number of topics I've mastered through the

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knowledge check. One thing you can do to get

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extra practice is you can just click on start my

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path. And ALEKS will start asking you questions.

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Presumably, in order of the topics, it felt that

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you did not show sufficient mastery of when you

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completed that knowledge check. Now you do have

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some more control over what you want to learn.

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And so if I go up to the top left corner, there

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are those three horizontal bars, I'll click on

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that. And when I click on that, I get a whole

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bunch of options here. And I'm just going to

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explain the first two options. If you want to

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learn a new topic, you can click on learn. And

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if I click this down menu here, you can actually

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go along and pick what you want to learn. And

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you can even pick the topic. So for example, I

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can click on real numbers. And before, it lets

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me go too much further. It wants me to master

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applying the percent equation. And but there

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could be also be other options off to the right.

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And let me just see if I go for example here.

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And another topic, there's more than one option.

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So it doesn't want me to move on until I get

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this one correct. But that's not always going to

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be the case. Now, what if you've mastered a

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topic, but you start realizing that Yeah, you

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got that question? Right on the knowledge check.

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But, you know, do I really do I really

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understand and maybe maybe a little more

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practice, and I can really nail it and really,

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fully master that topic. If you go to review,

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and click on review.

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Again, you can now you can review the topics

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that you've mastered. And so if I click that

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down arrow, so this comes up, I go up to here,

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where it says review, so it's reviewing all the

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topics, I click on real numbers. And now I can

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review the questions that I got right and you

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see, it's got a little crown icon, or at least I

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think it's a crown icon, and it says Master, so

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you can see that you've mastered that topic. So

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go to work. See what you can do. If you have any

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trouble, please reach out to me or check some of

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the walkthroughs and that and the help. that's

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available on Moodle and the ALEKS website