 We'll change now. There we go. Are you still there, Lizzie? Yes, I'm still here. I was just preparing my environment as well. Okay, not a problem. Let me know if that you struggle with. Okay. I'll be here until job takes over. No problem. Actually, I should be fine. I should be fine. If you want to leave, you can leave any moment. Just share my screen and then we should be off. And good afternoon, everyone. I hope you are able to unmute and greet me as well. Because I want to hear from you. I don't want to be the only person talking. Guys, it's going to be one and a half hour of long silence. Then if you're not going to talk to me, are you able to also put something in the chat? Hi, everyone. Hi. Yes. Thank you. Hello. Hello. I just put on my video for now so that you can see who you will be talking to for the rest of the year or the semester or whenever the sessions end. That's me. I'm going to turn off my video because where I'm seated actually is not conducive enough for a video. As you can see also the light is reflecting on the wall and my wall is just blue. So I'm just going to turn it off. Maybe the next session I will have a nice environment where I can also show you my face again. So welcome to the basic numeracy class or session. I don't know. Like I said, 2022 started very wrong for me. That says basic statistics skills. No, don't worry about that. It should say basic numeracy skill online sessions. Always when you come to class, you must always remember to switch off your video, mute your microphone like you have muted your microphone all along. Thank you. And there will be a register in the chat. Make sure that you always complete the register. I'm going to place the register now in the chat. While we speak, then you can also because I haven't started with anything. While I do the introduction, then you can complete the register. You can also post it closer to the end of the session for those who join late. Just make sure that before you leave, you complete the register. It's very important to complete that register. Because in order for UNISA to continue offering this sessions, they need to know that students are attending the sessions. And we're not just saying we're offering this and then there is nobody. I'm here alone. So the register helps with that and also it also helps with sending out information. For example, if in the session now when I explain certain things and then you ask me and I say I will send you some information like I will send you additional information. I will send it to UNISA and UNISA can distribute it to everyone who was in class. The only way to know who was here is via the register. So if your name was not there, you won't receive that information as well. So make sure that you complete the register. Please don't put your student number on the chat. There is a register. You just put in your student number on the register and select the correct session for today. There are a couple of them. I don't know which one you're going to select, but I will suggest that you select the first one that says basic numeracy skills by Ms. E. Boy. Don't select the second one where it says basic numeracy for economics management science by Mrs. L. Boy. That very long one, you can ignore that. You need to select the one that says basic numeracy skills, Ms. E. Boy. Okay, so that is all about introducing you to the house rules. If there is any question, administrative questions that you didn't get the link, you don't know where to find the notes. You don't know where the recordings are. You can send an email to CTNTAT at unisa.ac.z. All sessions are recorded. And the recordings are made available after 48 hours or more. I think it's even more than 48 hours, after 48 hours or more. So allow two to three days at least for the recordings to be available. But it's always good that you must be present in the session so that you are able to get first hand information and not wait for the recording. If you have any content related questions, like we're doing something here and you don't know what is happening, you can send me an email. That is my email address. E-boy.em at unisa.ac.za. Or if you have an assignment question and you can see that assignments are due very soon and we are not covering any topics related to the assignment, please just get hold of me or send me your questions and I should be able to assist you. Hey, so like formally welcome to your skills numeracy class. This is the first session for 2022. Normally there is a session plan that tells you the topics that we're going to cover to be covering every month. I will do that as soon as possible. But for now, bear with me, we will do topic by topic as we go along. I haven't completed my session plan as yet, but as soon as I have that documented, I will circulate it and you will have access to it as well. This session, I'm going to explain to you what these sessions are all about later on. Today is just, we're going to take it very easy. I'm not sure if you have been with me previously or this is your first time because you don't want to also unmute yourself so that you can talk to me. I was hoping that we can have those engagement as well so that I can understand your expectation and I can also tell you my expectation. Okay. And my name is Elizabeth Boy. I'm going to be your facilitator for the rest of the sessions for this year. You can call me Elizabeth. You can call me Lizzie like Adele called me Lizzie, but you can use any name you want. Please don't call me Mem. I'm not Mem. I'm not old. I'm still very young. I'm very young to be called Mem. I'm also just to clarify certain things. I'm also not a teacher. I'm not a lecturer. I am just a facilitator. I'm here to facilitate the sessions. So any UNISA related issues, even though I use UNISA email, I'm not UNISA employee full-time. I do have a day-to-day job. I work at the University of the West End Cape, but with UNISA I've been there with them for about more than 18 years now counting. I'm doing the same thing that I have been doing, but even improving as we go along. So I've started as a tutor with statistics and be a new, and then I moved into numeracy facilitation as well. So not that I want to break about anything, but yeah, I have been with UNISA for that many, many years. Facilitating the sessions. And like I said, I work at the University of the West End Cape. But I don't also do anything related to lecturing or anything like that. I work in the RFTAS office. I do business intelligence reporting and analytics. So I lead the BUI team at UWC. And that's me. And that's the way when I hear about me telling you about myself. And today is the last time you hear about that. So we go into start with the orientation. What is this classes? These are not tutorial classes. These are numeracy classes. What does that mean? You will notice that some of you are doing QMI, some of you are doing BNU. We combine both of you in the same section. So here we're not going to talk about BNU. We're not going to talk about QMI. We're going to talk about numeracies. And what is this numeracy? And numeracy involves the ability. So we want to impart you with the abilities to think and communicate using numbers. We want you to be able to make sense of the data that you're looking at or the numbers that you are looking at. And also have a spatial awareness of what is happening around you and understand patterns and sequence. Sometimes we will get to those things. But we're not going to do as they are described in the textbook as well. But we're going to give you the skills in terms of how do you identify certain things and how do you solve them. We're going to also make sure that you are able to recognize situations where you need mathematical reasoning that you can apply when you want to solve certain problems. And this will go even in the range of how you want to solve problems in your assignment. And when you go to the exam, how do you even answer your exam paper? So we impart you with those skills. So like I said, it's not module related. We're not going to talk about QMI. We're not going to go through your study guide. We're not going to read line by line what your lecturer is putting in your study guide. That's not the papers of this session. That is the tutorial papers. Yeah, we're talking about skills. I'm going to unpack to you the skills of how to unpack a question, how to use your calculator, how to manage your time when you are working through your numeracy module, which is QMI or BNU, and how to solve those problems. What are the shortcuts of answering certain questions when you are asked? Those are the things that I'm going to help you with. And with that, because we're talking about numeracy, we can cover a range of topics like we can cover topics such as measurement, algebra, charts, coordinates, where we talk about line graphs, numbers, volume. It's where we talk about measurement, simple interest or amortization when we talk about financial meds. We're going to cover topics relating to functions, equations, and today, because it's introduction, just to make sure that everybody is at ease and everybody is able to do or apply some of the skills and answer numerical questions, we're going to start with the basic skills. And most of your modules cover this part of your introduction, but here we're just going to quickly run through it and then the following sessions we can see what kind of skills can we impart in terms of different topics within the numeracy space. So we will cover a lot other than those ones that I've placed here, but all of the topics that we're going to cover in this session are related to your two modules, either to be a new or related to QMI. So they are there to assist you to navigate both of your modules. So in this session, like I said, we focus on identifying the skills that the students need and how did I do that to identify that there are gaps? Like I said, I have been here for more than 18 years, so it means being a tutor in class concentrating on content, I realized that students are struggling with basic skills of answering questions, basic skills when it comes to the content. Sometimes the module expects you to do certain calculations, but there are still foundational skills that you need to understand before you can answer that question. And I saw that if we can address those gaps, then students will do better in these modules, like especially students who have never done maths before and they are enrolled in QMI or BNU, we are able to bridge that gap. We are going to present to you or provide you with a range of strategies. I might give you multiple ways of doing certain things. You need to choose the one that you feel comfortable with. In maths, we say there are many ways to skin a cat. And if someone in the group has been exposed to another method that I'm not going to share, you are more than welcome to say, let's do it this way because I think this is the easy way. And we can follow what you are doing. I will narrate it on the board when you are explaining it and you can share it on the chat and then we can help other students. So the purpose of these sessions as well are to assist one another. It's not me talking all the time. It's you doing the work and you assisting one another as well. And then I will also provide you with activities like any other activities to do. I will do explain some certain concepts so that you can understand. And then we do a lot of activities. And then the other thing, what I want to do this year is also to introduce the numeracy in your context, in the environment that you are in. So if you work in the health sector, I want to bring the health sector information into the forefront so that you can see how you can apply the same information that you are using. Because I realized that in the timetable it's always about numbers and formulas, but it's never been explained in a way that you can understand that, oh, this actually relates to if I'm at work, this I can apply and use the same concept to do certain work. And that's what these numeracy skills are all about. But we're not going to divert a lot from your module. It will still cover what you need to know about your module and help you to go and write the exam. Okay, so like I said, I'm going to share with you some strategies. And this is one of those strategies that from now on going forward, I'm going to use this strategy. I use Newman Error Analysis Prompt for answering numeracy questions. So what this framework does is that it allows you to think about the question, analyze it, find information that will help you to answer the problem and then solve the problem. And after that, you need to go back and reflect on that problem or give feedback or get feedback on that problem. And that's what we're going to be doing in the whole session. So what it does, the whole framework, I want us, when we answer any question throughout, even you can apply this method in any of the modules that you are doing, whether it is a finance module, whether it is law module, whether it is English module, you can still apply the same because what it does, it says, let's read the question that we are given and make sure that we read it and understand it in our own way. So you will read it and interpret it in the way you feel that, oh, you understand the question is asking you. And then you're going to ask yourself, what does this question ask in you to do? And those are the things that you're going to pick up. Either the question is going to ask you to solve something, to describe something, to manipulate something, to change something. So that is what the question is asking you. And those things help in terms of how you're going to solve the question. Then you also need to identify things in the question. Tell me how are you going to find the answer. So identify things that will help you to answer that question. For example, what formula do I need? What information is given in that question? So if you apply that and you collect all this information and write it down some way. And that is where drawing comes in. You need to write it down. What is given? What formula can I use? Because based on what is given, you can identify what formula you need to be using. And based on what the question is asking you to do, if the question is asking you to manipulate something, it doesn't require you to use a formula. And then you just manipulate that thing. And then once you have done processing those, sorry, once you have done transforming and looking for facts, then you can start processing. By processing it means you can start now calculating, driving now, starting to write down how you answer the question. Formula and then put the calculator, the values in the calculator and calculate and then that's it. And once you are done, then you go back and reflect on that. Did I do everything correctly? Am I having the right answer? Look at the question. Did the answer, do I need the answer to be in two decimal or in one decimal? And then you are done. And that is the method that I want you to start using when we go through this whole context, content. This is the framework. It looks in a graphical form. If you want to take a picture of it, you can take a picture of it. So we're going to read the question in our own understanding and write it or understand it in our own words. Then we go into ask ourselves, what does this question want me to do? Does it want me to solve for X? Does it want me to manipulate? Does it want me to change the subject? Does it want me to derive? Does it want me to prove all those things? You ask yourself that. And you also going to ask yourself, how am I going to answer this? By means of going and looking at, is there a formula? But before you get to how am I going to answer this, you're going to identify the important facts. The important facts are the things that are given in your statement. Am I given the value of Y? Am I given the value of X? What is it that I am given? Am I told what X is equals to? Am I given additional information? You write it down. Everything that is given. And then once you wrote everything, you can even draw a picture or you need to write everything down. Given, if you are doing geometry, then you can say, what is it that is given in this picture? Am I given an angle? What is this angle? And this angle is equal to how many degrees and so forth. You identify and you write everything down. Once you are done, then you ask yourself, is there a formula that I can use to answer this question? And then you go and get the formula. You're not, when you get the question, you don't go and start answering the question. You need to first do this process before you get to doing the calculation. Once you have identified the formula, then you start doing the calculation. And sometimes the calculation, it means writing it down on a piece of paper before you take your calculator and start calculating. What I've realized previously is that students will just go into the calculator mode without writing everything down. You need to start writing everything step by step in a format that you're going to follow and then use your calculator to do the calculations. But you need to visualize everything that you are doing before you can take your calculator and start calculating. And that is a practice that you need to apply so that when you revise closer to the exam, you would have forgotten everything I told you today. But once you have written everything down, when you revise, it's easy to go back and reflect on what you have written because now you have step by step information that you can go back and go through it so that you can know and remember or refresh your mind in terms of, oh, how do we answer this question? Oh, yeah, we do this and this and this. Then you can go and take a calculator and see if you get the same answer. And that's how it will be easier for you when you do your revision. I'm almost done. And once you are done with that, you can check your answer and you can ask other people to help you check your answer. Now, here is the other thing. When you send me information for me to check whether you are doing the right thing, you cannot send me a question and say, I'm getting the answer that I'm getting is two. I can't help you. I need to be able to see how you got to that two before I can respond to say, oh, you went wrong here. Oh, you missed something here. Oh, you needed to do this, yeah. I need to be able to see where is the gap? Where are you getting it wrong? I don't want to see your answers alone. And later on, I'm going to share with you the WhatsApp groups. We can also have a discussion offline from here on the WhatsApp group. If you have any question, you can post it there, but you also remember, you can't just post a question without showing how you did it. Post a question, show us how you're doing it, and then we can comment on it. Don't compare options. What did you get with option A? For question Y, one, what did you get? What option did you get? It doesn't help you. It doesn't prepare you to go write the exam. So we do everything step by step. We show how we have evidence of how we did this, what was the outcome, and then we get feedback on that. And that's how I want us to work going forward. Even here, we're going to do the same. We're going to follow the same thing, the same theory that I just gave you now. We're going to do that. Now, in terms of how we're going to work going forward, your schedule, I think now is no longer called my UNISA, but the schedule, the notes, the recordings are posted on my module. That used to be my UNISA on my module. The interaction every Monday, except when it is a public holiday, like this next week Monday, it's the Monday, so there is no class. The next session will be the 25th of April. We're going to meet here on MST. That's where we're going to meet every Monday. And any comments, any questions? Any question? Because I only have one minute before I start with numeresis. Any question? You can unmute yourself. Let me see if I'm not alone in this room. Because you might find that I am talking to myself. You can unmute and talk to me. And please remember to complete the register. I see that Jack has also attached the... Oh, yes. Has posted the attendance register. Hi, guys. How are we going to work? So my expectation of this session is... I'm a very nice and loud and fast-talking lady. But I don't want to be the only person head on this recording. I want the sessions. I know those who previously attended my sessions know this. I want the sessions to be interactive. I want people to be able to share their ideas. I want you to talk to me. I want you to tell me if I am going fast. I am going too slow. Oh, you don't understand anything. If I need to repeat something. So what are your expectations? What do you expect since you came? Oh, you just signed in because they sent you the link. And you just wanted to see what is happening. What do you expect to gain out of these sessions after I have just spoken for almost 30 minutes? You can... Win threat. You can unmute and talk. Good evening. Hi, everyone. Hi. Okay, so I will go first. I think for me, I'm doing QMI. So for me, I'm looking forward to these sessions because I find that I struggle with the format of the assignment and exam questions just to sort of break it down. So, yeah. Is it first time doing QMI? It's my first time doing QMI. I did be in EU last year. And I found that when I would go through the study material, I was able to do the activities, but as soon as I would do assignments and exams, it's quite difficult to sort of decipher. Okay. Yeah. Thank you. Thank you. Any other person who wants to say something? So I guess Nombulello is doing QMI and BNU. Okay. I would like to say that I am repeating BNU at that time. I did eight modules, I think, in 2020. And I failed to pass six. So now last year, I had like a break. I'm a full-time mom, wife. I work full-time. So, yeah, I'm studying part-time. So it was quite easy. But now I'm trying to do the classes. And because I find that I have a better understanding when I do attend the class, which gives me a score at the end of the day. Yeah. Okay. All right. Thank you for sharing those you have shared. I am also a student. I know your frustration. Waking and studying at the same time is not a child's play. And especially now when you say you are doing eight modules and you are waking full-time, it must have been hectic. But yeah. So when you attend these sessions as well, you get the opportunity to ask questions and to get clarity on things that you don't understand. When you go listen to the recordings, you don't get that person saying, oh, but then the way you understood the question the first time is not correct. So you're just listening to a conversation that people are having, but you're not engaging because you still have those things that you don't understand. And nobody can tell you where are you going wrong with those. So it's easy when it's this engagement, then we can reflect on those challenges that you have and then help you along the way as well as quickly before you get into more and more and more challenging problems as well. And you must also remember that with numeracy, if you get the basic right, everything will be fine because it's a build up and everything are almost like interlinked. So today we're going to look at the basic, basic things that you need to know because based on that, it will determine how you answer the questions going forward as well. So let's get to the concept of basic numeracies. So we're going to, you will require sometimes not today. Today it might not be necessary for a calculator, but you do require a calculator to do numeracy because numeracy is met. And with numeracy, when you do a module like BNU or QMI, you need to practice. You cannot study. So the more you practice, the more you feel comfortable answering the questions as well. So today for this hour, I want us to concentrate on these basic skills and see how far we get and how easy it becomes for you to understand how you're going to work through your module as well. So we're going to learn how to apply the bot mass rule. It's very, very important, especially in your module like BNU or QMI. It's very important that you know this rule and you know how to apply it because you are going to be manipulating equations. Some equation will have brackets, some equation will have multiplication and divisions. If you don't understand the bot mass rule, you won't get the answers correctly because it is the foundation of manipulation of equations or solving equations where you have basic operations. Then we're going to look at the powers and then the roots and then we're going to look at how we change the subject of the formula. Later on, when we look at functions, when we look at linear equations, when we do simultaneous equations, then you will have already grasped the understanding of manipulating the equations by changing the subject of the formula. And you will be doing changing subject of the formula for the entire duration of the module because even when you do financial calculations, you are going to be manipulating the equations. Sometimes they might ask you to find the number of years, sometimes they might ask you to find the interest. It means you're going to have to manipulate that formula that they have given you. So you need to know these basic skills in order for you to do any thing that you need to do in your module. So bot mass rule. What does bot mass rule mean? Bot mass rule, there are other rules or laws of numeracy that you can use like associative law or distributive law. You can use them. But I think bot mass rule helps you to deal with equations that are more complex as well because with bot mass rule it says brackets first. So you need to first remove the brackets. So if the equation that you are working with has brackets, you need to remove those brackets. Then in the previous years when we were growing up we used to say this is off which represented multiplication of something but in terms of evolution. Now this is your powers. So I'm just going to say powers or exponents. Your all represent powers or exponents and your D represent division and your M represent multiplication. Your A represent addition and S represent subtraction. So what does that mean? It means if I have an equation where I have a bracket, a division, an addition it says I must first solve the bracket first. What is inside the bracket first? I must then do division first then go and do addition. Now if I have an equation that has division and multiplication, the law says division and multiplication have the same priority. They have the same priority. Therefore when I work the equation where I have a bracket, division and multiplication so if I have a bracket and I have a division and then in the next one I have a multiplication it says I must just work from left to right. So I must first deal with the bracket then do division and then do multiplication. If I have the same, I have a multiplication and division it says I must just continue working from left to right because division and multiplication have the same priority so therefore it means any equation that have both of them I can just solve it from left to right. Addition and subtraction also same concepts. They have the same priority. Therefore it means I can solve them from left to right whether the equation start with a subtraction and then goes to the addition. I must just solve the equation from left to right. So let's begin this example that we have here. We have number one. It says solve the following expression. 36 multiplied by 8 minus 34 multiplied by 8. We need to look at the Bodmer's rule. Bodmer's rule says brackets first, powers before division and multiplication and division and multiplication before addition and subtraction. So the equation has a multiplication and multiplication and a subtraction. So therefore a Bodmer's rule says I must do multiplication before subtraction. So it means I must multiply 36 multiplied by 8 and also I must do 34 multiplied by 8 before I can subtract. So what is 38 multiplied by 8? 36 multiplied by 8. 288. 288, subtract. 34 multiplied by 8. 272. 272 and that will be equals to 288 minus 272. 16. It's equals to 60. And that's how you will apply the Bodmer's rule. So you must always ask yourself, what basic operations am I given? Addition, subtraction, multiplication, division, what does it mean? Division and multiplication comes before addition and subtraction. So therefore it means I must do multiplication first before I do subtraction. If I had division and multiplication, then I can do from left to right. Okay, let's look at this next exercise. So if you look at the following exercise, it says simplify or solve the following expression. And this expression has seven multiplied by open bracket, six multiplied by open bracket, six plus four, close bracket, plus three multiplied by open bracket, two plus one, close bracket, close bracket. So we need to always go back to the Bodmer's rule. Bodmer's rule says bracket first. So here we have three brackets, brackets inside the brackets. So it means the outside bracket, we cannot solve that before we solve the inside bracket. So let's solve this bracket and that bracket first. That is Bodmer's rule. Because this says I must solve this. So it means identifying what I need to be doing is the Bodmer's. Brackets comes first, but I have three brackets. I've got the big bracket, then I've got this bracket, the first bracket and the second bracket. I need to first solve the small brackets. So let's solve the small brackets. Seven multiplied by, we don't even have to do the multiply by, because it's also included, multiplied by six, multiplied by solving the first bracket. Five plus four is nine, plus three times solving the next bracket. Two plus one is three, close bracket, because I removed this bracket, so I must close the bracket. So I still have a bracket. Bodmer's rule says I must remove bracket before I do addition and subtraction, because then I've got multiplication, multiplication, addition and multiplication inside the bracket. So first I must remove what is inside the bracket. What is inside the bracket? I have multiplication, addition and multiplication. Therefore it means I must apply the Bodmer's rule again. Multiplication before addition. So I must do the multiplication first. Seven times. I'm still going to put the bracket, because I'm resolving only the multiplications. Six times nine. What is six times nine? 54. That is 54. Oh, sorry. I must not close the bracket. Plus three times nine. Three times nine. Sorry, three times three. Three times three is nine. It's nine. Close bracket. And then I have 54 plus nine. So I have seven times. Sixty three. And what is, and that is equals to 441. Right? Yes. And that's how you apply Bodmer's rule. Remember today we're going to take it slow. We're not in a hurry for anything. We're just applying the skill that you need to learn. You can go and practice with your module as well, in terms of mobile activities. Let's look at powers. What do we mean by powers? So powers, the way to represent a value multiplied by itself so many times. So if I have two multiplied by two, instead of writing two multiplied by two, I can say this is the same as two to the power of two, because there is two multiplying itself two times. That is a power. And with the power, we can define each of these elements. The one at the top, we call it an exponent or power. And the one at the bottom, we call this a base. It's important to remember all this, because there are rules that you need to apply if you're working with powers as well. But today we're not going to talk about those rules in detail. And I just want to share with you, is you need to know all these things when you're manipulating your equations and expressions. So what are those rules or laws that you need to always remember? There are certain things that you always have to remember when you're working with powers. Now, the first one is that if I have the powers with the same base, so we're going to use X's as our same base. And if we, let's not use X, because I want to say multiply and if I multiply, let's use A, A and B as our letters. Let's say A, multiply by A, but this is A to the power of 2 times A to the power of 3. It says if I have exponents with the same base or powers with the same base, the rule says I must just add the powers. So this will be 2 plus 3. Let me call it the rule or a law. You can call it anywhere you want. So if I have the same base, I just need to, and I'm multiplying. So if I need to find the product of two bases or two powers with the same bases, I just add the exponents. And if A divides, if I need to find the quotient, and this is 3 and this is 2, I'm just going to interchange the two. If I have to find the quotient of the two values, or two powers with the same bases, the rule or the law says I need to just subtract the exponents. And you need to simplify this further because A to the power 2 plus 3 is the same as A to the power of 5. A to the power 3 minus 2 is the same as A to the power of 1. And we're going to get there just now. Also the law says if I have X over Y to the power of 3, the law says I can distribute the power to every base. So yeah, the bases are not the same. So I'm just going to distribute the power so you can write this as X to the power of 3 divided by Y to the power of 3. That's it. So if I have A to the power of 2 to the power of 3, the rule says I also can multiply or distribute the power by multiplying. So this will be the same as A to the power of 2 times 3. She's the same as A to the power of 6. So you can also simplify all this to A to the power of 1 and so forth. And those are the rules. There are also certain things that you also need to take into consideration when you work with powers. So yeah, it's when you only multiply, dividing, or you have a power raised to the power. Then you can apply all this. When you manipulate the equation, for example, this is A to the power of the power of 1. Sometimes any value without a power, please take note. So this is where you need to take note, take note. Any value to the power of 1, we can write it. If A is any number, any number to the power of 1, we can write it as that number. Any value to the power of 1, you can write it as A. So this A to the power of 1 is the same as A. But A to the power of 0 is equals to 1. That means 100 to the power of 0 is 1. 200 to the power of 0 is 1. 300 to the power of 0 is 1. 1000 to the power of 0 is 1. So any value or any number to the power of 0 will be equals to 1. The other thing that you also need to remember, which you're going to do very soon, any number to the power of a negative value. So A to the power of a negative 1, let's say. We can write this as a fractional number. So this will be 1 over A. So any value 1 over A can be written as A to the power of a negative 1. So a negative 1 will represent 1 over. However, let's assume that I have A to the power of negative 3. If I have A to the power of negative 3, you cannot write this as 3 over A. Nope, it's not the same. That's not the same thing. A to the power of negative 3 is the same as A to the power of... Sorry, 1 over A to the power of 3. Only the negative is 1 over. Just that negative. That's that. Because remember A to the power of 1 will be the same as A. So that's why you will have just 1 over A. This is very important, especially those ones who are doing QMI, because when you go and do differentiation, you need to always be able to apply these rules. When you do differentiation, you need to be able to apply all this. It's very important. But when we get to differentiation, and we go to topics like that, I will bring this up again. Like I said, I didn't want to spend too much time on this. Let's get on with it. So any number to the square root or to the root, so let's say A to the root of 2, which is the square root, any value to the root or any value to a square root or any root can be written as... This root, we can write it as a power of a half. So the root, this root is 1 over, and whatever the value that is in front of the root will be underneath the 1 over. What do I mean? So if I have the root, the cube root of A, I can write this as A to the power 1 over 3. If I have the root of 4 of A, I can write it as 1 over... A to the power of... A to the power of 1 over 4. And that is the powers. So now, I think I have said a lot. Let's determine the following values for this. Now, I have been using A as a variable. Now you need to use the actual value. Remember, any value to the power of A number, it means that number multiplying by itself so many times. So what is 2 to the power of 3 is the same as 2 times 2, which is equals to 8. Sometimes it's going to be very difficult for you to answer questions like that. What if they say it is 2 to the power of 16? You cannot go on and on and on and on and on and write in 2 times 2 times 2 times 2 times 2 times 2 times 2 until you get 16 of them. Your calculators have the functionality. Depending on the type of a calculator that you're using, when we get to a session where we go and do calculators and you don't know how to use your calculator, we're going to show you how to use your calculator. So on your calculator, depending, because different people use different calculators and today we're not talking about calculators, you do have x to the power of 2 as a button. Sometimes you do have x to the power of y or y to the power of x. I don't know how it looks. Those who are using k-sure, you do have x to the power of 2 and then you do have an x to the power of a bloggie. So x to the power of 2 gives you a power of 2, your square. It's your square of the value. x to the power of y or y to the power of x and x to the power of a bloggie will give you any value, any power. Power of 4, power of 3, power of 6, you can use any of these two functions. Depending on the button on your calculator, if your calculator button is written in orange, whatever the function that you are looking at is written in orange, you need to...