Nov 19 Video 1 Exponent Laws pages 12-14

beep and here we are so we were talking about this yesterday and this is where my pen crapped out when we were talking about bases and exponents yes and the difference between this which has how many bait how many different parts to the base here come in if needed apparently not um how many different parts are there in the base here no one just the x how many parts are in the base here two what is the mathematical thing that makes the green one have two parts of the base seth the three and the x are in brackets brackets group in math any time you see brackets around anything that is one thing even if it's got more than one part does everybody understand what i mean hey miss can everybody understands yeah even if i and you don't need to write this down x squared plus seven x if there's brackets around it that's one thing okay and it moves around as a group if you knew that x equal 2 then this would be uh for 18 right it would be one thing everybody's cool yeah that's what brackets do all right so um the next thing of course is power and that's everything a power is a base and and i see i'm yelling there and an exponent okay we always talk about just the exponent as being the power it's not the whole thing is and you read that as base whatever the base is to the um nth whatever the power is power so this is seven to the third um eight with a nine up there would be eight to the ninth right you all know this already this is grade nine stuff you don't need to worry about about um wasting a lot of time brain power on this because you already know it but there are two special names and that is squared and cubed they get special names everything else we read it as to the whatever power fifth sixth eighth okay all right now i am going to turn off the screen and you are going to fill in this chart carefully now i'm going to do the first one so you know what i'm talking about here is you fill in the blanks so we have a power here yes what's the base two what's the exponent four what does that actually mean two times two times two times two which is not eight what is it sixteen is everybody good fill in this chart go sum um if when you get out to the far right where it says evaluate if you don't know how to do use your calculator to do the big numbers you can leave that blank if you don't remember um i'm thinking of the fourth row down right that's going to be a very big number and some of you may not remember how to do that on your calculator but i'll we'll talk about that when the time comes do so cabbages no one lettuce cabbages never mind there's the right answers i've highlighted all those in blue for a reason there's something i want to talk about with all those blue ones so check your work make sure you have done um done everything okay and then ask if you need to ask so i'm going to let you ask first and then i'm going to talk about why i highlighted all those in blue does everybody remember how to do number eight how to make your calculator give you the answer everybody and by by giving you the answer i mean you didn't go 8 times 8 times 8 times 8 times 8 you use the exponent button right everybody knows how to use it no somewhere on your calculator seth there will be an x with a y above it or a y with an x above it or something that looks like this a little mountain are you is he using his phone oh no there's an exponent button on there somewhere on there it looks like this seth it's either x with a little y y with the little x you found it no not an e with an x or this little mountain boxes it might be x with a little box above it because they've had to do that because people are so bad word bad at math that they've have to do this one time summer i've even seen this blank with a blank above it oh yeah because people oh my god letters and math letters are for reading but you know in today's current climate i don't even think letters are for reading because nobody actually reads any information they just see whatever headlines some po somebody posted on their anti-social media then that must be true right because if it's on the internet it's true world's flat well it must be the way listen to people talk in the streets all right so anyway did you find the button there seth no well we'll talk about it later we almost never use that button don't worry about it jake we'll find it later it's there trust me i'm going to be like your mom and i'll be like if i come over there and find it oh yeah summer knows that gang i can't find by any socks mom did you look no it's funny of course she finds it because we look summer we don't go like this no socks we move things [Music] lies all right there's an old tv show that has an episode like that um the guy in it is looking for his keys and the the show opens he's looking around he can't find his keys anywhere he leaves the room and then some guy runs out and puts his keys on the desk and runs away and he comes back in he says because the guy that's looking for his keys is living in a tv show and he doesn't know like that movie the truman show and that but the gag is all of us are living in a simulation yeah and there's people doing and like the the guys that made the set forgot to put the keys there so they run out and put it there now when did that show come out 1955. they were already thinking of the matrix in 1955. anyways sorry back to math it's one of my favorite episodes of that show all right here we go uh so why is that first one highlighted because of this right is there a bracket around the negative so what's the base there it's only the three and the base is what's repeated 3 times 3 times 3 and 3 times 3 times 3 is 27 yes but remember this actually means negative 1 times 3 cubed so here is the negative 1. so negative one times 27 gives me negative 27. okay oh i made a mistake there shoot that's supposed to be positive sorry everyone no i was in the negative vibe because i was highlighting um and this one of course the negative is in the brackets yes so it's negative negative which gets you a positive yes right now what if i made this three what would be here another negative five and would this answer be positive or negative negative it would be negative 125. everybody cool all right so we're good now down to here negative 1 because the negative went again and again and again it's part of the base now since it had an odd exponent the answer is negative what if i added another negative one there then this would become positive one right everyone's good okay then we're good down to the next blue one we should be good down to there why did i have to leave this as xxx because i don't know the number which is why i also couldn't evaluate it could i you can't tell me what that is because i didn't tell you what x is and then this one always messes kids up how do i have positive base and a positive exponent and end up with a negative i gotta have the negative one out front but this one's weird because if i did negative two oh there goes my early today nice nice good technology always saves the day oh it won't even let me close it today awesome solid uh if i did negative two to the fifth would i get the same value you don't just get to say yes and no and wait if i change this to this so you you guys argue about that for a minute while i try to get my uh purple dot back would this highlighted in green get me the same value out here yes why because it's an odd exponent right but remember so negative two to the fifth equals negative two to the fifth they're the same thing when you evaluate them when you write them out they're totally different does everybody understand that spectacular and then everybody understands why there are two nines and two ways to get nine there's a third way to get nine we could have done nine to the one right so everyone's good with the rest of them and everyone's good with this one in particular the negative repeats six times so it should be positive but there's a negative out in front so that wins at the end is everybody good with this chart okay now this chart should have been pretty much what you did in the ninth grade right yes except some of you may not have done that row but i think i asked yesterday and everybody did do some work with that in grade nine so that row is grade ten we almost never will be using numbers in grade ten it's almost all going to be variables is everybody okay with that all right so let's turn the page over to page 13. now everything on page 13 you should already know but i've got to make sure because as i i have learned in 22 years of teaching even though there are only seven things you need to know about exponents for some strange reason it's always poorly done no matter how i teach it no matter who teaches it it's poorly done because in grade 11 i get kids from all the other math teachers and they all stink at exponents whether they were taught by me george charlie uh mr snickel fritz who cares they all all kids stink at exponents and i don't know why because there's only seven things that can happen and if you write down what is actually going on it makes perfect sense so we're gonna start real slow with stuff that you already know so i'm gonna multiply powers of the same base did i tell you what the base is no so what do we give it in math when i don't give you a number a letter and kids always say x all right so we'll stick with x x is a base everyone agree now you can give me a number for the exponent somebody say a number what 7 is too big i don't want to write it out that much it has to be under 4 2 times x to the fourth are they the same base yes they are the same base now every one of you is going to say what's the answer all of you should know this x to the power of six right mescan why is it because you add the exponents or is adding the exponents what you do in this case does everybody understand the subtle difference in what i said okay what you do here is you add them but that's not why it sticks adding them is the shortcut and when you only learn the shortcuts that's why when i give you a really big exponent question that's why you guys screw it up because you're only learning the shortcuts you're not learning what's actually happening everybody cool so what is actually happening here is what is that really x times x yes times what is that really x times x times x times x right multiply multiply multiply multiply multiply have i repeated my multiplication so that becomes x to the sixth right trust me i know it seems stupid to learn it this way when all i need to say is add the exponents but trust me this is what you need to know so then we can come out here and do exactly what muscan said because she's absolutely right x to the a x to any exponent times that same base to any other exponent is x to the a plus b easy peasy right now you're in the 10th grade you learned to add in kindergarten right can you forget in the 10th grade how addition works no you can't does everything you've learned in math apply to the very next thing you learn in math you can't forget previous stuff can you so let's pretend this was totally new to you right can you forget about it when we get down to number six or something no so be careful that's the next thing that causes trouble with exponents i can in one question use all seven of these and that's why exponents gets difficult okay all the rules apply all the time okay all right so the second one easy peasy we're gonna use x again we're going to use we're going to reverse this instead of x uh squared times x to the fourth we're going to do x to the fourth divided by x squared now the next problem that you kids have is you don't recognize the different ways this can be written right this is the same as x to the fourth with a slash and it's the same as x to the fourth over x squared because this symbol divided by is a fraction right something divided by something all right everybody good now you're smart young people what is the inverse of multiplying dividing when we multiplied we added so what is the inverse of adding subtraction so the shortcut here is subtract yes but what is really happening what does this really mean what does that mean [Music] 4x yes x4 x's over what does that really mean x times x what is x divided by x no what is 6 divided by 6 one what is seven divided by seven one so what is x divided by x one so this becomes one now you all wanna cross it out because it's cancelled has it really disappeared no that's why i don't like using the word cancel it's not gone it's just a one now so this is one times x times x times x do we write one times anything no that's why you cross it out now but when you cross it out it makes you think it's not there anymore you have to be careful with that so what's going to happen here with this x and this x that's going to be one again right what's left two x's which is x squared easy peasy lemon squeezy right and the rule if i have x to the a divided by x to the b i do x to the a minus b easy right my pen is slowing down so i am going to risk shutting off uh one note now before it freezes and bringing one note back that'll show you all right we're all good yeah okay so the next one and we'll keep with uh three and four or four and two oops i like doing those black x to the four squared now again you all already know the law you know what the answer is here i know you know the answer but i want to you to tell me why what is the base here this is tricky x to the power of 4 is the base isn't it and how many times does that base repeat twice so this really means x to the fourth oh it froze anyway every good thing i said about that there because it was awesome that's the best i've ever done that now nobody it's heavy rain with the sun shining through it it's not snowing it's eight degrees out there water doesn't freeze till zero all right now ladies and gentlemen you're going to notice that every law now from here on i'm going to stop you along the way and i'm going to remind you that all the previous laws still apply all right so if i gave you this x squared y cubed squared how many ways could you and i don't want you to write down all the ways but how many ways could we write this down can somebody tell me one way i could write this differently than what i've done here and still have the same value seth i could have gone x x y y y and squared yes yes okay what could i do with that i could write it again because it's squared right so i could write x x y y y x x y y y now how many x's do i have four and how many y's do i have six frozen oh but this one maybe it'll work because it flicked out yeah buddy now that's what's actually happening yes but does exponent law three apply here look back to exponent law three when i'm going over a bracket what did i do in exponent law three multiplied so isn't this x two times two x to the fourth and isn't two times three x y to the sixth so we're good yeah now there is one thing that you all screw up here if i give you this and i'm going to blame i wonder if it's this stupid purple circle that's causing me trouble anyway if i gave you this 2 x squared y squared squared what would that answer be remember all your math applies and you don't need to write down the work you could just write down the answer if you can get it in your head that's cool too but bear in mind i wrote this one down because this is when kids screw up all the time anybody want to risk an answer what is it seth is it like 2 times x to the 4 times y so close and that's the mistake kids make every kid remembers to do that but isn't that 2 part of the base so shouldn't that 2 also get squared so it is 4 x squared y squared kids always forget that in the 10th grade okay uh my scan i'm just getting to that now some kids will write two squared x squared y squared right mascan i owe you four dollars but i owe jj two squared dollars which one's easier four always if you can evaluate does everybody understand would i dock marks here do you think if the question were out of four do you think i would give you four out of four remember you guys were all in elementary school four meant you were exceeding expectations yes now that's a stupid way to measure math right because to exceed expectations in math what is the expectation in math to get the answer right three plus four equals seven can you get a four can you exceed my expectations when i ask you to add no of course not it's impossible but because the education system lumps everything together and refuses to understand that math and science are different than socials in english we are forced to adopt this stupid policy of exceeding my expectations you can't exceed expectations in math you can get the answer right or not so technically is it possible to get a four in math is it possible no do i make it possible yes if the answer is absolutely perfect you have done every mathematical thing you can do i will give you four out of four does everybody understand so would this be four out of four no because you can do something you could make the two squared that this is four out of four this is three and a half does everybody understand and i'm sorry but i've heard rumors that that is the way it is going you may very well be assessed in math by the time you leave high school on that one two three four scale which in math is idiotic but nobody asks math teachers why would we ask the experts right kind of like how fraser health knows who you guys are close contacts with in class all day right because i got a phrasal health person standing right here don't i who's checking who's sitting where right who does actually know who knows who you guys are in close contact with all day right now you and me do i get told if one of you gets or want a person from your family test positive no but that's that's that's a social studies question not a math question okay a fraction base we all know fractions scare us but they don't need to x over y squared now is this anything to be frightened about because isn't multiplying pretty closely related to dividing and aren't fractions just dividing and what did we do when we had multiple different bases in there and they were multiplied we just put the two to everything yes so what do you think we do here right that would be x over y times x over y which would be x squared over y squared the two goes everywhere do all the other rules still apply yes or no yes so what if i gave you this two x cubed y squared over x y squared does that talk about all six laws right now are they all in there is there some dividing is there some multiplying is there some uh exponents to multiple bases right so everything's there is there a right or wrong way to attack it no you just apply the laws in the order you see fit right so somebody tell me what you just tell me what would you do first my scan because i only because i couldn't hear you somewhere because you said add the exponents then you changed your mind and said something different i'm not being mean muscan what would you do [Music] so you would go inside here right okay so now that muscan has forced us into a path somebody take over from her it's like tag wrestling muscan's out somebody just hit her with a chair and she's reaching to tag at the ropes and she's tagging in seth seth what would you do now that mescana started down this path you would deal with this and this right so you would get two what would you do with x x three and x one get rid of the bottom you'd get rid of the bottom one and what would that become two so now i have x squared what would happen here to a one which we don't write yes and now all of that is squared now seth has been hit with a chair but muscan because wrestling is real has shaken off being hit with a chair and she's ready on the side to tag in and save seth who just got hit with a chair what would we do now yeah excellent now everybody agrees that's the right answer yeah now watch see if i can erase this without killing ah screw it 2 x squared y or x cubed y squared over x y squared right could i bring this 2 to everything now which would get me 4 x 6 y 4 over x squared y squared cancel 2 of those that becomes 4. cancel two of those that becomes two do i get the same answer does it matter which place i started no does everybody understand that's why teaching exponents is difficult there's no one path you can follow everybody you can take a different route and all of you may take a different route which is the second thing i need to say that's why showing your work is so important everybody cool all right that should be good everybody should know all of that from the ninth grade was any of that news excellent but it's nice to get the refresher let's talk about negative exponents did anybody do that in grade nine one two you did it a bit okay so remember how i said that knowing the exponent of zero was what would make you understand this right let's go back to that so we had three cubed which equaled 27. i'm not gonna bother with the three three three everybody's cool right three squared became nine and i'm dividing by three as i go down right three to the one was three three to the zero was one now four times in a row when i drop my exponent by one i divide by three yes so what is the next logical exponent one now we're gonna stop for a second if we were writing that middle column that had the repeated multiplication is there any way you can imagine writing three times itself negative one times could we write that in any way no we could could we how would you write that the last time that we couldn't write something was three to the zero yeah so what did we do we followed our pattern divide by three divide by three divide by three so we can't write it so what do we write here we divide by three what is it one third please notice it is still positive right now what is the next logical exponent what do i do here logically because i can't write the middle column i got to divide this by three yeah which would be the same as multiplying it by one-third which would be one-ninth yes what would the next one be 1 27 now please look 3 to the positive 3 27 how should we really write 27 but we're too lazy to write it that way what 27 over 1 right and look here what do you see what do you call this when you flip them somebody said it yesterday reciprocals right so x to the negative a equals 1 over x to the positive a and my screen just froze maybe we're back nope i like that you think i was actually gonna be able to hear that i was listening specially but please notice the color of my hair i am very very old the ears are one of the first things to go all right is everybody cool yeah now please notice it's still positive all right now the next thing requires you to um make a leap of understanding okay so let's do this x to the fourth divided by x to the sixth according to law number two what should you do there subtract so what would this answer be x to the negative two do negative exponents exist do they make any sense no we're never allowed to have a negative exponent so this is technically x over 1 right so what is this answer really how do i write it properly we just did it right there 1 over x squared is everybody cool now i want to show you something this means x to the fourth over x to the sixth yes which means x x x x over x x x x x x right what do we do to four of those x's cancel them out and they've all become ones yes so what's left on the top 1 because it's 1 times 1 times 1 times 1 times 1 which is 1 over what's left on the bottom x squared see does everybody see how this comes together all right my scan i'm gonna do a couple of questions that use all the laws in a second and i'm gonna show you the way a way to do it like we've been doing it all the way along okay now here's the next problem one of you understands that right i've asked like four times everybody's nodded you're all like yeah yeah i got it but then i do this what is one over x to the negative three danny pardon yep x cubed it just reciprocates because negative exponents are never allowed if they're already in the denominator they would move they would reciprocate is everybody good yeah but you got to be careful doing that too and you'll see why right okay so i'm going to slide off to the side like i've been doing if you want to find some white space or some blank paper of your own to practice these that's cool but i personally believe that the most important thing you need to do right now is not try to copy down what i'm doing try to think through what you would do okay that's why i say don't write this next thing down there's tons of practice coming up that is written down in your book all so let's try five x cubed y squared times three x squared y cubed squared more than one way to start this but this one's really tricky because there actually is only one way to start this but then after that there's lots of things you could do what do you think you need to do first seth you've got to get rid of this one does that apply to orange purple or both just orange right so the purple one's not going to change 5 x cubed y squared what does the orange one become six x three squared is six i told you someone would do it to the 4y to the 6. now what combine the two so what am i going to do with that and that add multiply it's 5 times 9 isn't it so what is it 45 x what 7 y what 8. now was any of that math difficult math no of course not how many of you said the wrong thing at least once see what i mean the math isn't hard right you can't tell me the math is difficult but putting it all together becomes problematic right when i asked what 5 and 9 was if i just wrote 5 9 all of you would say 45 you multiply it but because we're talking about exponents some of you said add right that's what i mean can you forget the seventh grade where you learned that if you write two numbers right beside each other it's times can you forget that no that's previous math and does all previous math apply right everybody good all right let's make a small change to this question not that that's too big a change we're going to erase all this look at how slow it's erasing this is a pc the hard to get touch screen all right now i'm going to make a very small change negative two now there's a ton of different ways you could start this would anybody like to say what they would do first yes you did start the last one seth smart move to always volunteer on the first one because you know it's always the easiest miss scam what would you do first and you've been the first one in the ring a few times so way to go so you would deal with that two first okay so you would have five x cubed y squared 9 x to the what no no danny what 4 negative 4 because you multiply over here yes and y to the 4 then what would you do combine the two so it would be 45 x to the what negative one right y to the sixth is that allowed so what how would you finish this off 45 where would this go denominator because you reciprocate it x y to the sixth is everybody cool now could you do this a different way could you have moved this two right away down here and then this would have been down here right x to the fourth and then everything else would have been the same i would have had three x's in the numerator right there four in the denominator canceled them and left me with one for one x down there is everybody good please notice how many different ways you can do these questions you have to decide the way you would do it right now do you think i follow the same path every time of course not because let me give you an example again and you don't need to write this one down either what if i'd add 3x cubed y to the sixth over 6 x to the ninth y to the 12th all of that to the negative two what is something you could do part of me you could do inside right now couldn't you and that would get you one over two three-sixths one-half three and nine if there's three up top and there's nine down below i can get rid of those three and i can get rid of how many of these three so that would be x to the what sixth and if there's six up there and twelve down there i can get rid of those six what's down here six now all of that is to what power negative two because i didn't touch that one yet right now what stop it what does it now again could i bring that negative exponent everywhere inside could i but that would mean i would have one one two three four negative exponents is that a pain it is but doesn't a negative exponent reciprocate its base so couldn't i write this as if i could write through this [Music] couldn't i reciprocate that base yes so i would get 2x to the sixth y to the sixth over one yes and all of that would be what would be to what exponent positive two now it's super easy isn't it what's two squared 4 what's x to the 6th squared no 12 right because it's 6 times 2. and y to the 12th does everybody understand now watch right here could i not also have done 1 to the negative 2 2 to the negative 2 x to the negative 12 and y to the negative 12. could i have done that and then all these negative exponents have to switch don't they so this 2 would come up and become 2 to the 2 x to the 12 y to the 12 over 1 to the two do we ever write one as a denominator no and two squared is four and you see you get the same answer does it matter what directions you go no do you have to apply everything yes yes is everybody ready to try yeah you are the first work you do is super easy 35 questions they're all you can do in your head page 15 and there's like three or there's six questions on page 16. uh 15 minutes go we'll mark it in 15. not for marx you'll just see it you're if you're doing it right or not okay go while i try to get my piece of crap machine working okay the next thing to try might be this pen uh you don't need to show your work on this page because it's all in your head right yeah feel free to close those all the time ladies and gentlemen that is totally up to you

Channel: Matt Myers

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Id: B3eeNzcoX20

Length: 52min 41sec (3161 seconds)

Published: Thu Nov 19 2020