03 - Exponents and Order of Operations in Algebra

hello and welcome to the section of the algebra tutor in this section we're going to talk about what we call exponents and order of operations has a fancy sounding title I promise you that by the end of it you'll be understanding things that you never really thought would be so easy to grasp through a bunch of example problems this is the first section in this sequence where we're really going to start doing some things that sort of resemble algebra a lot of students get turned off to algebra in the beginning because they open the book and they see all of these symbols and things they've never seen before exponents numbers raised up high parentheses all kinds of things that you normally don't see until you get sort of into an algebra level right so we're going to break these things down we're going to talk about what exponents are and make sure you really understand and then we're going to get into order of operations which tells you how to calculate things in algebra and what comes first what comes second I'm not going to bore you with a long list of rules we're gonna do it by working problems so what is an exponent an exponent is a big word that just means it's a shorthand way of writing multiplication it's a shorthand way of writing multiplication let me show you what I'm talking about here if you see something in a book that looks like this four with a two on the top this is an exponent the two is what we call an exponent and it's a shorthand way of writing this four times the dot is times four right so we call this four squared anytime you see a 2 up there it means squared it just means that you take the bottom number and you multiply it by itself as many times as is indicated in the exponent so it's four times four so in this case four times four is 16 so 4 squared or 4 raised to the power of two is 16 so for those of you that that are scared and terrified of algebra you should look at this and realize it's something you can understand this 2 is not magical it is just 4 multiplied by itself two times there four squared so likewise 4 raised to the power of three would be 4 times 4 times 4 right you multiply by itself three times because that's the number indicated at the top and it can be any number you want it could be you know 59 raised to the fourth power right and that would be 59 multiplied by 59 multiplied by 59 multiplied by 59 now this is a very large number take these numbers and multiply them in your calculator you're gonna get a giant number this is why we used exponents it's kind of a big pain to keep writing this multiplication out we can write it like this and wrap it up much much smaller and keep it nice and neat instead of writing all this multiplication out everywhere so that's what an exponent is that's the basic basic picture one thing you must make sure that you do not give into the trap of is making the following mistake do not make the following mistake four squared for instance is not that means not equal to four times two a lot of students will look at these numbers and say well 4 times 2 that's 8 well that's wrong because we already said that 4 squared is equal to 4 times 4 4 times 4 is 16 4 times 2 is 8 so you can see that these two things are not equal so you definitely don't just multiply by the exponent and you're and you're done what you're doing is you're multiplying the bottom number here by itself as many times as indicated by the number up there so we already talked about it but I'll just write it down so for instance or squared is equal to 4 times 4 is equal to 16 that's how you get that all right let's do another one let's say we have 6 squared what would that be equal to that would be 6 x by itself 2 times because that's the number here 6 times 6 is going to give us 36 you can see right away that 6 times 2 if you just did that would be 12 that's nothing even close to 36 so just forget about multiplying these you have to multiply by itself now it does not matter what number you have here it could be a fraction it can be a decimal to be anything so let's use parentheses for the first time in this class and we'll take the fraction 1/10 and we'll raise it to the power of 4 do not get scared by parentheses parentheses is something we're going to use a lot in this section parentheses is one of those things that scare a lot of students like whoa parentheses they belong in an English book they don't belong in a math class parentheses in math basically means that whatever is inside you want to kind of keep it together right in this case the power of four applies to the entire thing inside of here and since a fraction is kind of this complicated thing we wrap it in parentheses here to indicate that the entire thing here is raised to the fourth power it's kind of like you can think of it like a little plastic baggie or something you want to put a bunch of chips in a plastic baggie to carry it to a picnic you don't want them spilling everywhere right if you have a large term that you want to kind of keep together in one unit you just put parentheses around it to keep it there as a unit so that you know when you're looking at it that everything you're doing to that is is applied to everything inside the parentheses that's the only reason we're using it so in this case what this is going to be is to use parentheses again to get you familiar with it one-tenth right multiplied by 1/10 multiplied by 1/10 multiplied by 1/10 now I'm putting a dot in here but really when you put parentheses right next to each other like that it means multiplication but for now I'll just keep putting the dots so this is exactly what you might expect just like we were doing six up here six times six well this is what's inside so it's 1/10 times 1/10 times 1/10 times 1/10 we're doing it four times because we have a power of 4 there now we have actually done this kind of multiplication in the previous section on fractions you know that when you're multiplying fractions all you do is multiply the top numbers so one times one times one times one is just going to be 1 on the top 10 times 10 times 10 times 10 if you do that in the calculator is 10,000 so if you actually go to a calculator and take the fraction 1/10 and raise it to the fourth power you're going to get the fraction one ten thousandth right one ten thousands so that's basically showing you that anything inside of your raised to a power basically all behaves the same way now let me show you something quickly that's that's interesting when you have something like this 1/10 raised to the fourth power 1/10 raised to the fourth power it's exactly the same thing this exponent can apply to the top and to the bottom set so it's one to the fourth power ten to the fourth power it's the same thing they're basically equal I'm kind of teaching you a little bit of different rules as we go here that you'll pick up as we do more and more problems but anytime you have a fraction like this with an exponent applied you can apply the fraction so the exponent to the top and the exponent to the bottom separately to make sure you understand that what is 1 raised to the fourth power think about it what is 1 race to the 4th power that's 1 times 1 times 1 times 1 which is 1 so that would be 1 on the top what is 10 raised to the fourth power that would be 10 times 10 times 10 times 10 we've already done 10 times 10 times 10 times 10 we figured out that that was 10,000 so we get the same answer either way if you're gonna break it up like this you get this answer if you're gonna apply the exponent to the top and the bottom you get exactly the same answer they're both equivalent all right so let's do one more of those to drill that in if you had the fraction 1/2 and you raise that to the 6th power you could say 1/2 times 1/2 times 1/2 times 1/2 times 1/2 times 1/2 you can write all that out that's fine that's no problem but we can also write it as 1 raised to the 6th power over 2 raised to the 6th power we effectively can apply this exponent to the top and to the bottom when we're raising fractions to exponents like this so on the top what do you think 1 to the 6th is gonna be it's gonna be 1 times 1 times 1 times 1 times 1 times 1 so we're gonna get 1 on the bottom let me write it out 2 times 2 times 2 times 2 times 2 times 2 because we're multiplying the twos together 6 times when you do that to calculator you're gonna get 160 fourths so if you were to take 1/2 and raise it to the 6th power you would get 160 fourths all right now I want to switch gears a little bit we've talked a little bit about exponents I think I've given you enough examples that you understand what an exponent is and why it's useful it certainly isn't nice to keep writing this multiplication out we wrap things up in exponents to keep them nice and tidy and once you know what they mean it's really not a big deal to understand next I want to talk to you about the term that you'll see a lot in algebra it's called factor let me write that down real quick a factor I am NOT going to give you a book definition for a factor I'm going to give you Jason's definition because my definition I think is a little easier to understand even though it's not as as a is nicely worded as a book it is something that you multiply together to get a result in a nutshell factors are things that are multiplied together that's that's really the bottom line so for instance if I had x squared now we're actually diving into the realm of algebra a little bit using a actual letter don't get worried about letters letters are not a big deal to worry about in algebra all you're basically saying X is we could represent any number X could be 1 X could be 5 X could be negative 3 X could be 1.4 X could be anything so we don't know what it is so we just keep it as X and we just going to leave it like that but you also know that anytime you raise a number which is what X really is to a power of two it's the same as x times X this is coming straight from the definition of what an exponent is so these X's here these are what we call the factors so these are what we call the factors this is really just a definition to be honest with you you're not going to you're going to use factors a lot in algebra but if this is more of just getting the definition drilled into you they're factors because these are the things we multiply together to kind of get what we will be started with basically let me give you another couple of examples and I think you'll see if I have a 3 Z to the fourth power how do I write this well it's going to be 3 times Z is raised to the 4th 3 has nothing to do with this exponent Z is the thing that's raised to the 4th so it's Z times Z times Z times Z so the 3 is multiplied by Z times Z times Z times Z all these things here that are multiplied together they're just called factors just trying to give you some examples in fact they're called the product of factors because product means multiplied they're these are the factors multiplied together to give you what you started with now what if I had open parentheses five times T squared when I write two things next to one another like five and T with nothing in between it always means multiplication anytime you see two things I'm sitting next to one another in algebra you got to get used to the fact that you're not going to always see multiplication symbols everywhere if things are sitting next to each other you just need to assume that they're multiplied together but in this case five T is raised to the power of two but it's inside a parenthesis this means that this exponent applies to everything in here so it would be five T times 5 T so 5 times T times 5 times T basically and these are the factors these are the things that are multiplied together to give you that notice that that's a little different than above here we didn't have any parenthesis so the exponent only applied to the Z but here the parenthesis are forcing the exponent to apply to everything inside and that's another reason why parentheses are so useful let me switch colors here just to break it up a little bit let's say we have five parenthesis 2 X to the third power how do you think that's going to be written 2 X to the third power well like I said the 5 is sitting next to something without anything in between so it's you should really think of it as being multiplied together and this is all raised to the third power so this is going to be 5 times 2x times 2x times 2x I'm multiplying 2x times itself 3 times because that's the exponent 5 is multiplied by everything because it's just sitting next to the parenthesis there and the 2x the exponent is applying to the 2x as a whole unit because it's wrapped up in these parenthesis the parenthesis like a little sandwich bag everything in there has to kind of sort of stay together more or less and everything on the outside like this exponent is going to apply to that whole thing all right so we've talked about quite a bit of stuff we've talked about exponents we've talked about the factors when you multiply them together these are just labeled factors that's just more or less to help you when your book starts talking later on about factoring expressions or telling them what the factors are and a test you'll know what they're talking about they just mean things that you multiply together to get you know what you're started with or whatever term you have now we want to do something practical now what we want to do is let's pretend we're just plug in let's say that X is known to be 3 and let's say that Y is known to be 2 so what I want to do is evaluate the following terms for x squared so we remember anytime you see a letter in algebra it just means that it represents a number that number is something that you don't necessarily know later on down the road we might use an equation to solve for that number right whatever X is we're just trying to figure out what it is in this case we're actually given that X is equal to 3 and Y is equal to 2 so if we have what we call an expression this is just a word that means you know something you write down that you need to evaluate we call it an expression what we need to do is take the value of 3 and stick it everywhere we see X everywhere we see X and evaluate the results so what we'll have is 4 times 3 squared right that's what we're doing here 3 goes in for X so we're squaring them so this is 4 times 3 times 3 because 3 squared is 3 times 3 so starting from left to right 4 times 3 is 12 so we have to continue we put 12 here because that's equal to 12 times 3 12 times 3 is 36 so the answer is 36 all right okay now the next thing we need to do just as another example is say what about 5y raised to the third power how do we do that well we know that Y is equal to 2 so let's go ahead and put it in there five times remember this is an implied multiplication because they're sitting next to one another - raised to the 3rd power so what we need to do is evaluate this and figure out what this is equal to now in a minute we're going to actually get to what we call order of operations and I'm gonna list and tell you exactly the order in which you do every calculation in algebra but for now I'm gonna give you the biggest most important rule that you can follow and I'm gonna drill this in because it's just so important always always always always do whatever is in the parentheses first I'll say it again anytime you see anything to calculate if you see parentheses you must you must you must do what is inside the parentheses first you always have to do what's inside the parentheses first it always comes first so that helps because here we're not sure what do we do the exponents or do we do the multiplication inside the parentheses well the answer is you do inside the parentheses first five times two is ten the exponent is still long for the ride but we've evaluated what's inside of here made it ten now we have ten cubed which is 10 times 10 times 10 10 times 10 times 10 and when you take 10 times 10 you'll get a hundred of course you still got one more 10 - x + 100 times 10 is a thousand and that is the answer so if you take five Y or Y is equal to two and you raise the whole thing to the third power you'll get 1000 you must do what's inside the parentheses first that's why we did this 10 first and then we raised the result so so so important we're gonna get to a little bit more of that here in a minute as well all right what if we have two X raised to the Y power now this looks more complicated right but don't worry about it it's like a jigsaw puzzle you just put in what you know two times you have two time multiplier because it's a implied multiplication because it's sitting there X is three raised to the Y power which is two so we just plug the numbers in there okay now the other thing is and I'm gonna get to a whole list of whatever operations in a minute exponents come right after the parentheses as far as what's most important to do in this case there's no parenthesis anywhere so we have to worry about parentheses the next most important thing to do is the exponents so that's very very important because when you look at this you might say well maybe I multiply two times three and I get six and then I take six and raise it to the power of two but that's not right you have to do the exponent first which is three squared which is three times three right so what we'll have is two times three times three that's what we're gonna get and then what we're gonna have is two times three is six six times three so we'll do it like this is six times three is eighteen so we evaluate the exponent first writing it like this and then we do the multiplication left to right two times three is six and then with six times three here is 18 and that is the answer so always evaluate the exponent first so as far as the hierarchy goes I'll write it down in a minute parenthesis comes first exponents come next and then everything else will fall out after that we'll just see how it goes all right let me change colors real quick what if we have 3y raised to the power of X and notice that in this case three wives wrapped up in a parenthesis so 3 times y Y is 2 raised to the power of X which is 3 that's how we're writing this and now you need to think about you know a lot of students will be like well do I do the exponent first or do I multiply first well we already said that we always do what's in the parenthesis first always 3 times 2 is 6 now that 6 was what was in here it's all raised to the 3 power now we know exactly what to do because this is 6 times 6 times 6 6 times 6 is 36 still have to multiply by my final 6 6 times 36 is 216 and this is the final answer 216 so plug in the values evaluate what's in the parentheses and then do the exponent and that's gonna get you very far now I've kind of hinted I wanted to introduce you to thanks first before hitting you over the head with a bunch of rules but now we're going to actually tackle the topic of what we call order of operations we've actually been doing a little bit of it already never told you I'd kind of snuck it in there to kind of make you comfortable with it in your book a lot of times whatever book you're using will list order of operations I'll give you a list a mile long of things for you to memorize I'm gonna make it much easier than that for you so here we go order of operations order of operations basically you you need to have some kind of list to tell you what order to calculate things otherwise you're gonna get the wrong answer so the first thing you do is what we talked about parentheses are the most important thing if you see parentheses anywhere in any calculation you must do what's inside the parentheses first always okay that's very easy to remember when you when you really do it for me the next most important thing to do is exponents so if you have parentheses do them first after that if you see any exponents anywhere do them next if there are no parentheses anywhere in what you're doing then you do exponents first so it's a it's a list a priority list of what you do okay the next thing you do is multiplication and division if you have any multiplication and division and after that the most or I should say the least important quote-unquote thing is add and subtract all right folks that is my list of word of operations your textbook might have a longer list trying to make things you know pretty with special rules and things to remember and all that and I'm gonna drill in how to do this for you with example so you won't actually have to memorize the list but hopefully you've memorized enough to know that the parentheses always come first the exponents come next then if you have any multiplication and division you do them and then if you have any addition and subtraction you do those dead last you might think addition and subtraction are so important but in fact they come dead last never do any addition or subtraction until you've done everything else now there's one sort of exception to this whole thing if any of these things like let's say you have some addition and subtraction wrapped up inside of some parentheses right you have to do what's inside the print these first so you do that first so this priority order makes sense but I'm just telling you if you have any of things these things lying inside of a parenthesis set then you just do those first because it follows rule number one trumps everything else all right so let's get some practice I'm a firm believer in learn by doing we can talk and talk and talk and talk but if I just show you a few examples it'll be so easy let's say we have 3 times 5 minus 4 and I'm asking you let's do this calculation well the first thing you do is you say well there's no parenthesis anywhere okay that's great there's no exponents anywhere okay that's great I'll look for multiplication and division I see hey here's the multiplication so I do it 3 times 5 is 15 you have to keep this along for the ride because you haven't done them yet now you look at this and you say well the only thing left is subtraction I can do that because there's nothing else to do 15 minus 4 is 11 bingo you've got your first answer very simple all right now let's take something a little bit different let's say we have 3 parentheses 5 minus 4 now the first thing you do is you say well do I have any parentheses and you say yes I do now this is a great example inside of these parentheses is subtraction which I told you was dead last however since it's inside of a parentheses said it takes priority and you do it first so we always do this first inside the parentheses so we keep the 3 along for the ride keep our parentheses 5 minus 4 is 1 now this is just straight multiplication there's nothing else to do so 3 times 1 is 3 that is the final answer okay now let's say you have 3 plus 5 squared this is an excellent example of one order of operations and must be followed let me show you how to do it properly first you look for parentheses and there's no parentheses so you're okay then you look for exponents and you look here and you say ok 5 squared I need to do that guy next so I'll keep the 3 plus 5 squared what do you think 5 squared is that's 5 times 5 you're multiplying it you know 2 times there so 5 times 5 that's 25 now all I have is addition it's dead last I can do that 3 plus 25 is 28 and this is the final answer 28 now if you did this incorrectly if you don't follow this list you might just try to add 3 plus 5 and get in get 8 and then you'll try to apply the exponent 8 squared 8 times 8 is 64 that's nowhere close to the correct answer so you cannot just start adding things and doing things in any order you want you're gonna get the wrong answer you must do it in this order exponents first and in addition switch colors for a minute let's say we have 2 plus 3 times 5 minus 4 2 plus 3 times 5 minus 4 now we're starting to get a little more complicated you might look at this and you say well maybe I shouldn't add 2 plus 3 and then multiply by 5 and then subtract 4 but that isn't not correct you look through your list any exponents no any parentheses I should say first parentheses and open it's nope look for multiplication and division I have multiplication going on right here I must do him next 2 plus 3 times 5 gives me 3 times 5 gives me 15 minus 4 comes along for the ride now the only thing you have left is addition and subtraction which is dead last that's okay now when you have addition and subtraction on the same level with no other parentheses or anything you just do them left to right like reading a book all right so 2 plus 15 is 17 you still have to subtract your 4 17 minus 4 is going to give you 13 and 13 is the final answer all right let's do another let's say we have 64 divided by 3 plus 1 how would we do that well the first thing we do we see this division we might be tempted to do something with that first but we see the parentheses first we must do parentheses first so 60s 4 divided by and what is 3 plus 1 3 plus 1 is 4 now I have a straight division problem I can obviously do that there's nothing left to do 64 divided by 4 is going to give me 16 and that is the final answer 64 divided by 4 is going to give me 6 all right we'll do one more on this board we'll have 7 plus 9 divided by 2 times 4 so we notice we have lots of parentheses here so we can do the parentheses kind of imperil L if we want we can do this parenthesis in this parenthesis in the same steps we just need to make sure that they're done at the top of the list 7 plus 9 is 16 divided by 2 times 4 is 8 we must do what's in the parenthesis first we did do them first we just did them at the same step that's okay to do all right so we have 16 divided by 8 there's nothing else to do here so we have 2 now what we're gonna do now is we race the board do a couple more quick examples involving order of operations to wrap a section up okay what if we have 5 plus 7 divided by 3 times 4 so the first thing we do is try to look for parentheses and we see that we have parentheses so we do that first 5 plus 7 is going to give us 12 so we're just writing 12 we carry the rest of the problem along for the ride so we look for parentheses first here we don't have any print C's left we don't have any exponents so we look for multiplication and division and in fact we have a multiplication and division on the same level so we do them a left to right like reading a book 12 divided by 3 is 4 we still have to multiply by fourth in 4 times 4 is 16 and 16 is the answer all right what if we have something that looks complicated but really isn't 100 divided by 10 times 10 divided by 100 so it looks really complicated but you just kind of go through it check for any parentheses we don't have any parentheses check for any exponents we don't have any exponents check for multiplication and division we have lots of multiplication and division so we do them all left to right on the same level so 100 divided by 10 is gonna give us 10 I have to carry the rest along for the ride I haven't done anything with that Wow same thing here we do left to right 10 times 10 gives us 100 and I carry this along for the ride and then finally the only thing left to do is do this division which gives you 1 and this is the final answer all right well do one last one of this type and show you that you really can't understand this stuff because it's not that hard it's gonna look hard you know if you never took algebra I never watch this lesson but it's not a big deal three squared plus two parentheses 1 plus 4 minus 2 looks very very difficult at first if you especially if you haven't taken algebra books because you've got an exponent you've got parentheses and you've got subtraction in addition all at the same time you might you know if you didn't know what any of this stuff was you might start adding things out of order and really getting yourself into trouble so the first thing to do is look for parentheses we see we have a parentheses here so we'll just rewrite the rest of the problem and do inside the parentheses first 1 plus 4 is 5 everything else is rewritten now we look now this is a parentheses but there's nothing to do it's just a number so this is really just multiplication so the next thing we do is we look for exponents here's an exponent 3 squared what do you think that's gonna be 3 times 3 it's gonna give us 9 plus 2 times 5 minus 2 I'm just rewriting taking the parentheses out because it's just multiplication now so here we have 9 plus 2 times 5 minus 2 and you might be tempted to add 9 plus 2 but that's gonna be wrong because you need to look in your order are there any parentheses no are there any exponents no is there any multiplication and division yes there is it's right here we must do that first 9 plus 2 times 5 gives us 10 now the only thing we have is addition and subtraction they're on the same level so we read it like a book left to right 9 plus 10 is 19 carry the 2 along for the ride 19 minus 2 17 so if you take this monster and put it into a calculator you'll get 17 as an answer if you start doing this stuff out of order you will definitely not get the right answer all right we want to do one more problem type will wrap up this entire section just kind of building the complexity a little bit none of this stuff is hard but you do need to see a lot of practice so let's pretend that X is equal to three this is given to us Y is equal to two it's given to us Z is equal to four this is given to us and for the first problem let's evaluate this expression five Z divided by two plus y5 z divided by two plus y so the first thing you do is plug in what you know 5 z 5 times Z would be 5 times z which is 4 divided by 2 plus y which is 2 so we've converted everything over to numbers and now we go through our order of operations are there any parentheses no are there any exponents no is there any multiplication and division yes there is there's multiplication here and there's no vision here so we do those first so let's start left to right 5 times 4 is 20 let's rewrite the problem did this making it 20 now we again see we have division that's gonna take priority 20 divided by 2 is 10 and this is just staying along for the ride now this is the only thing left to do so we did 12 10 plus 2 is 12 and that's the answer looks really complicated but you'll see that it's really not and let's do 3 2 X plus y all wrapped up inside of parentheses so let's plug in what we know we have 3/2 times X X in this case is 3 plus y Y in this case is 2 and all of this stuff is inside parentheses though this is another great example the first thing you do is you check for what's inside parentheses and we have a bunch of stuff inside parentheses so we know we have to do that first but what we have inside of the parentheses is a combination of multiplication and addition and you should know by now that multiplication takes priority over addition so we do the multiplication inside here first so the way you would write this is 2 times 3 is 6 keep the 2 along for the ride for the next step again we're gonna do what's inside the parentheses six plus two is eight now the only thing left to do is this multiplication 8 times 3 is 24 and 24 is the final answer all right let's do the next guide here we have x times y times Z plus Z squared minus 4x now this would give a lot of students a lot of heartburn having you know if you haven't studied this because it just looks so complicated but just take it one step at a time first substitute what you know X is equal to 3 y is equal to 2 Z is equal to 4 since Z is 4 we're gonna have 4 squared here and since X was equal to 3 we're gonna have 3 here so the first thing to check for us to see do you have any parentheses and no you don't do you have any exponents yes you do so do that one X so we have 3 times 2 times 4 don't mess with that stuff yet what is this 4 squared 4 times 4 is 16 keep everything along L everything else for the right don't do anything yet now we go back through it no parentheses no exponents do we have any addition or I'm sorry do we have any multiplication or division that's the next most important thing we have lots of multiplication here so let's do that stuff so we have is 3 times 2 is 6 but 6 times 4 is 24 so all of this multiplied together is going to give you 24 plus 16 and we can do this multiplication on the end 4 times 3 is 12 you know make sure you understand that all we did was do 3 times 2 is 6 times 4 is 24 the 16 stays where it is 4 times 3 can be multiplied together to give us 12 now we have a bunch of addition and subtraction which is dead last so we do it left to right like reading a book 24 plus 16 is 40 still have to subtract 12 and 40 minus 12 is 28 and that is the final answer all right here is the very last problem same values for the variables X is going to be equal to 3 y is equal to 2 Z is equal to 4 no changes everything's the same as before but here we're going to evaluate 2x plus y squared is equal to y plus 2 Z looks extremely complicated but it you'll find it's not a big deal 2 times X X is equal to 3 plus y squared Y is equal to 2 all divided by here we have Y which is 2 2 times Z which is 4 now this looks really really monster hair monster hair so the first thing you would do is look in your order of operations and see if you have any parentheses no you don't however there's something I really didn't want to write in my list but I want to tell you verbally anytime you have a big fraction this is what I call a big fraction we have a big fraction bar giant terms on the top lots of stuff on the bottom you kind need to treat the top and the bottom is having kind of implied parentheses they're not written here but you basically have to do the top and the bottom of the fraction separately before you can do the division that the fraction represents so I'm not going to draw it but you have to imagine some parentheses around the top and imagine some parentheses around the bottom then you will realize that you must do the top and get the top done and then the bottom separately done and then finish the problem out that helps you immensely and that's just sort of a rule of thumb you have to you have to remember so in the top what do I need to do in the top well there's you know the only the most important thing in the top is the exponent is highest on the list so I need to do that first 2 times 3 plus 2 squared 2 times 2 is 4 keep your fraction on the bottom what is most important on the bottom well multiplication comes more important than addition so let's do that first 2 times 4 is 8 now we continue working on the top this multiplication is more important in this division so we do that first 6 plus 4 we can just do this addition two plus eight is ten and now it's very simple six plus four on the top again is ten over ten now this is a division right that's what a fraction is ten divided by ten is one so that's a very very important rule of thumb for you to remember when you have a large fraction that's why we spent so much time on fractions in the last section to get you really comfortable with that but when you have large fractions like that you really need to consider the numerator at the top of it to have them like an implied parenthesis you must do what sort of like simplify everything on the top first and everything on the bottom independent of one another and then at the end do the division and that's just sort of the way it is so once we put everything in here we realize well the exponent was most important on the top so we did this guy and on the bottom the the the multiplication was more important than this addition so we did that and then when we got to this step the multiplication was more important in the addition so we did that and we did this addition on the bottom and then we did this addition and in the division and so on so that includes concludes this section we've done a tremendous amount of material a lot of people watching this have never heard of an exponent or get really terrified of parentheses I've tried to break down those barriers with lots of examples an exponent is just a short way to write lots and lots of multiplication parentheses are just used to group things together that's basically it the order of operations that we use as we do everything inside the parentheses first next we look at the exponents then we do multiplication and division and then we do addition and subtraction of course there's some exceptions when you have giant fractions you do you pretend that there's giant parentheses around the top and around the bottom so those come first once you're working on something inside of a parentheses set you need to follow the rules to figure out what to do first and second in this case the exponent was most important for instance right as you do more and more problems you'll get more and more comfortable with this so definitely watch this lesson as many times as you need practice every single problem in this lesson watch it a second time write these problems down as I'm writing them down solve them yourself there's dozens of problems in this section that if you master you'll definitely get it exponents an order of operations which honestly is some of the most important foundation to all of algebra so make sure you understand it follow me on to the subsequent sections we'll be taking our way through algebra step by step building up your confidence building up your skills and helping you to do well on your homework and on your exams

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Keywords: algebra, order of operations, exponents, pemdas, algebra 1, tutor, tutorial, lesson, algebra tutorial, math, order, operations, multiplication, division, addition, parentheses, arithmetic, order of operations with integers, order of operations algebra, algebra lesson, exponent lesson, review of exponents, what is an exponent, exponents and radicals, exponents and polynomials, exponents rules, exponents and roots, algebra 1 review, algebra 1 lessons

Id: yJaVfmEo0rI

Length: 39min 43sec (2383 seconds)

Published: Wed Aug 23 2017