(- 4 cubed / (-4) squared ) to the negative 2 power=? How to do this! MANY will get WRONG!

Рет қаралды 51,971

Күн бұрын

Пікірлер: 129

@johnclements6852 10 ай бұрын

Personally, I love the long-winded explanations. They really clarify the particular topic discussed, and my namesake John turns Math from something almost frightening to something friendly and welcoming. I'm 64, and Math has always been scary, particularly things like Algebra and Calculus, which I never studied as I left school to enter the workforce, but to my amazement and his credit, he made me begin to understand both within a couple of minutes of explanation. Well done, mate, regards from Christchurch NZ.

@stelun56 10 ай бұрын

SPURIOUS LONGWINDED EXPLANATIONS ARE NOT AESTHETICand good mathematics is always transparent and therefore lucidly clear

@stevenboese1480 10 ай бұрын

I remembered a movie called Stand and Deliver about a Hispanic teacher who went and Ap calculus in a LA school I think his name was Jaime Escalante the one scene I remembered was him saying " A negative times Negative equals a positive" he had the class repete this three times. He took a class of failing kids in his first year and they all passed but had to take the test again because the powers thought they cheated because of the work through were almost identical, they retook the test and some got a better score the the first time crazy right this just shows that a good teacher is worth more then they are getting paid. R.IP Mr. Escalante he passed last year I think ( movie stared Edward James Olmos as Mr. Escalante and Lou Diamond Phillips in 1988)

@remonalinton4808 10 ай бұрын

I was just looking at this math, and didn’t know to do. I’m adult student doing the GED. Thank you for breaking down the maths for me I really appreciate you❤

@nelsonfilho6779 10 ай бұрын

Parabéns por estudar depois de adulto. É difícil mas não é impossível. Força e resiliência pra você ! 👏

@thomasharding1838 3 ай бұрын

Good Luck to you! I think that is exactly why he makes these videos.

@TheAZZA0990 5 ай бұрын

1/16 , in my head in under 10 secs!! :) I am 85 y.o. and never went to Uni - but I have always adored mental maths and algebra!! ( And I say maths as a Brit!!! )

@eugengrzondziel1706 5 ай бұрын

Yes, we are to old for unnecessary complications😂 4^3=4^2*4 ALSO [-4^3/(-4)^2]= - 4 (-4)^-2= 1/4^2=1/16 i am 72

@Zhiroc 10 ай бұрын

BTW, the problem could have been more complicated if the powers weren't chosen such that sign ambiguity due to order of operations didn't mask it. For example, -4^3 could have two interpretations, either -(4^3) or (-4^3). But in this case, it doesn't matter. If a positive exponent were used, then the order of operations would matter. And then in this case, if the "outer" exponentiation would have been an odd negative power, e.g., -3, then this sign would matter.

@TheSimCaptain 10 ай бұрын

Yeah, many will have gotten this right for the wrong reasons. Should have been an even number in the exponent. His claim that not knowing this would lead to the wrong answer makes no sense.

@gavindeane3670 7 ай бұрын

Yes, it does seem a missed opportunity. He might just as well have had simply 4³ / 4². The two possible interpretations of -4³ aren't -(4³) and (-4³) though. Those are the same interpretation. The two possible interpretations are -(4³) and (-4)³.

@knutholt3486 10 ай бұрын

Much of the problems in this task is not only about mathematical logic as such, but about conventions of notation. I got it "right", but I had to think somewhat about what parts of the notations meant.

@seibertmccormick184 10 ай бұрын

Thanks for the refresher!

@Kualinar 6 ай бұрын

In my math courses, -4^3 was to be treated as (-4)^3, treating the minus as an unary operator, and unary operators have the highest priority, before parentheses. And, thus, -4^2 = -4 * -4 = 16, not -16. The sign inside the bracket don't mater. The result can only be positive. So... -4^3÷-4^2 = -4^(3-2) = -4^1 = -4. Finally, as x^-1 = 1/x. We finish this way, 1/(-4^2) = 1/16 In a test with multiple answers, if you don't know an answer, go to the few next ones. I very often found that subsequent question provided hint for previous ones, how to solve a previous question, if not the actual answer.

@Escviitash 10 ай бұрын

The exponent of the numerator is 2Z+1 so (-B)^E will be the same as -(B^E) both by value and signage, so you can't really make a mistake here. You could make an error in the numerator if the parenthesises wasn't there, as -(B^2Z) is negative and (-B)^2Z is positive. It is even worse if E is not an integer as (-B)^E would then be complex number. But the signage of the fraction doesn't actually matter as the outer exponent is 2Z, and any real number to the 2Z will be a positive real number, which means that you can completely ignore any signage inside any of brackets. The only thing that can go wrong here is if you don't know what X^(-Y) = 1/(X^Y). With that knowledge you can rewrite the problem to 1/((4^3)/(4^2))^2 = 1/(4^(3-2))^2 = 1/(4^1)^2 = 1/(4^2) = 1/16.

@johnnyragadoo2414 3 ай бұрын

Same base, top and bottom, so the answer has to be either positive or negative 4 to the 3-2 power. The top is negative and the bottom is positive, so that’s -4^1 or -4. To the -2 power is 1/(-4*-4), or 1/16.

@russelllomando8460 10 ай бұрын

Got it. A.... the final exponent makes it a fraction. Thanks for the fun.

@mudge40 10 ай бұрын

correct, negative exponents tell you that they are "under the line"

@davidsmith3736 10 ай бұрын

It was a good well timed refreasher,thank you.😊

@wcdaniel7 10 ай бұрын

Where did you solve for -4 exp 3 / -4 exp 2, both numerator and denominator to exp -2? 3 x-2=-6; 2 x-2=-4. -4 brought up to the numerator = -2 (-6 + 4). So, -4exp -2 = 1/-4exp 2 = 1/16.

@laurendoe168 10 ай бұрын

I effed up at the last step, forgetting -1/4 was in parentheses. I did -1/4 ^2 (which is -1/16) instead of (-1/4)^2.

@eddiefniii 10 ай бұрын

When would you use this?

@MadSlantedPowers 10 ай бұрын

This specific type of expression with these numbers? Who knows? Knowing how to evaluate something like this, however, is a good exercise in applying various mathematical rules. That way, if you ever find yourself working with some numbers or algebraic expressions, you will be able evaluate it correctly.

@robinblanc8208 10 ай бұрын

Great video!

@kennethwright870 10 ай бұрын

-4^-2=1/16

@MartinHermans-dw3is 10 ай бұрын

i always get your problems right buy this is the first one to stump me. I guess I needed that little review of using negative powers

@Hope-zf1bw 10 ай бұрын

I will get it wrong cuz I have NO IDEA what to do😅

@Kleermaker1000 4 ай бұрын

Ah, the brackets. :)

@richardcommins4926 10 ай бұрын

Yes, I got the answer of 1/16 in about 10 seconds in my head. But I have to comment that -4^3 does equal (-4)^3 so why make the distinction? Yes, I know that technically -4^3 really means an expression of (-1)*4^3 without the parenthesizes and not -4*-4*-4 but they are equivalent. You can just rewrite the expression to (-1)*4*(-1)*4*(-1)*4 and factor out the three -1's to (-1) to get (-1)*4^3. So why the distinction because they are equivalent? I solved the insides by using the formula a^c/a^b = a^(c-b) where a =-4, c=3 and b=2 for (-4)^1 by adding exponents then [-4^1]^-2 = 1/[-4^1]^2 and you multiply exponents to get 1/4^2 or 1/16. All you need is the laws of exponents to solve this problem in many ways.

@junerm21 10 ай бұрын

I got it right. I was a math teacher and a lady engineer.

@mauriziograndi1750 10 ай бұрын

With all respect for a video maker, mathematicians will never indulge in unnecessary manipulation. Video makers will.

@mavrosyvannah 10 ай бұрын

Who invented that formula in the end?

@s14tam 10 ай бұрын

Boy you really stretched out this one problem to fill 15 minutes... Instead of filling the video with so much fluff why not just work out more examples? It would be more helpful and less boring and I wouldn't have to skip over so much content.

@johnplong3644 10 ай бұрын

Many don’t have a clue as how to do this For those who do ,yeh it gets long and tedious .There are things you have to know to do this problem.

@johnplong3644 10 ай бұрын

Math Rebuild Corse how far does it go?? past Algebra 2? Trig up to and including pre- Calculus I am good in up to Algebra 1 and parts of Algebra 2 and parts of Trig Definitely need help in pre- calculus and of course Calculus I see you don’t offer anything in Calculus 1-4

@nitinvyas1950 10 ай бұрын

In competative exams, this method is much worst.....

@nitinvyas1950 10 ай бұрын

Give short cut to use it in competative examinations so candidates can solve in couple of seconds......

@olenfersoi8887 10 ай бұрын

You took an outrageous number of words to explain that with the neg 4 cubed, there are implied parentheses around the 4 cubed...such that it is -1 x the 4 cubed. In fact, dozens of your problems are constructed this way. In fact, there is no reason to write problems this way when the addition of parentheses, in the right places, & in most cases, eliminates the need to remember PEMDAS,

@terryjohinke8065 9 ай бұрын

I got -4^-2 = -4^ =-16 =1/16 . Sometimes I don't like your Methods. I use the index law. ( Ex Maths teacher From Australia)

@jillmondt5398 10 ай бұрын

Skip ahead to 4:10.

@champfisk5613 5 ай бұрын

Knowing the rules is key

@you6382tube 10 ай бұрын

4:14 starts

@arjunelatchman 10 ай бұрын

Great job sir.

@nelsonfilho6779 10 ай бұрын

Alternativa (a) 1/16 Boa questão !!! 🇧🇷 -4^-2 =-1/4^2 = 1/16 positivo.

@swampcat4901 10 ай бұрын

exp -2 already pointed out towards answer a)

@hotflashfoto 10 ай бұрын

Would you be kind enough to explain why the numerator is not considered "negative four cubed" but is "four cubed to the minus"? To me, seeing a number written as "-4" is "minus 4", aka "negative 4", and adding the exponent to it does not mean (to me) to raise the number 4 to the power without its sign, since the sign itself is part of the identity of the value. Without that sign it becomes an absolute value, which is different from what is written and inferred by what was written. At least to me, anyway. Can you explain it to me so I understand, please? I'm not a dummy, but it just doesn't make sense.

@MadSlantedPowers 10 ай бұрын

He kinda mentioned it in regards to the order of operations. The exponent applies to the number. You could also think of it as (-1)*(4)^3. Consider how you would evaluate 0-4^3 vs 0-(-4)^3.

@hotflashfoto 10 ай бұрын

I like your explanation. I apologize but this is a little wordy. (To simplify, I've left out the ^3.) Thinking of it as (-1)*(4) kinda makes sense, but not 0-4 since that changes it from me seeing the stated value of "negative four" to an expression that includes subtraction that is not in the original expression. Saying that it's "negative one (times) four" makes a bit more sense, however that also changes it by introducing multiplication that I did not see in the original expression. What I saw when I evaluated the original problem as written (and got the correct answer) was I envisioned the number 4 having two possible addresses. One is the positive value that is four units to the right of Zero on the number line and the other is four units to the left of Zero. To denote the positive one, we simply write "4" without the plus symbol, but to denote the one on the left we write "-4" and call it negative four, aka minus four. Writing -4 is not a mathematical expression on its own like 0-4 or -1*4 are. It's the value of a single number with the minus symbol telling you that the digit resides four units to the left of Zero. In order to write "(-1)*(4)" so as not to use negation on its own, one would have to write "(0-1)*(4)", and the original problem would have to be written out "(0-1)*(4^3)", but that undoes the whole reason for the video, which is PEMDAS, as well as some good entertainment and intelligent discussion. So, when I saw the original problem, his parentheses around the negative four on the denominator seemed optional to me. To calculate the numerator, it then became (-4)*(-4)*(-4). However, since I saw the denominator with the same base, I simply subtracted 2 from 3 and arrived at -4 for the new numerator and 1 for the new denominator. Then all I had to deal with was the negative power of the new expression of -4, and the only "math" I had to do was to subtract 2 from 3. If the original problem had had -4^2 in the numerator inside the square brackets, my final answer would have been negative 1/64 since the final value of the numerator would have been 16, not -16, making it equal to the denominator (in my estimation). And this is where the whole rub comes in and where it doesn't seem logical to me. I hope I've explained it clearly and without insults. @@MadSlantedPowers

@hotflashfoto 10 ай бұрын

Considering those last two expressions: 0-4^3 would be 4 cubed, and then subtract that from zero. The result would be -64. 0-(-4)^3 would be the quantity (negative 4) cubed that is then subtracted from zero. The result would be 64. The result of -64 is as I mentioned in my long-winded comment previously: a numerical value that lives at an address 64 units to the left of Zero. To me, the number is known as "negative 64", not "zero minus 64" by the way it is written. That is also how I consume it mathematically and logically. If I'm wrong, I'll accept that. This goes back to a similar video by Presh Tawalker. In those comments, it all boils down to the human just needing to be more careful about writing the expression in the first place. I write computer code throughout the day, and at times it includes formulas in both code, queries, and Excel cells. I'm OCD in being careful about not being lazy when writing my expressions because I don't want anyone (the computer or the next developer) to have any chance to misinterpret what is meant by my expression. In this way, I am certain to get the same result every time, no matter what. Relying on PEMDAS is for humans, not developers. That said, I'll rest my case and accept that, as a human, I may be mistaken in what I was taught. But as a developer, I am not. I write my code so as to be 100% crystal clear to prevent just such excursions and wasted time tracking down logic errors, which cost more time than most other errors do.@@MadSlantedPowers

@MadSlantedPowers 10 ай бұрын

@@hotflashfoto I guess I would consider -4^3 to be the opposite of 4^3. It's been a while since I wrote any code, but I have used Excel formulas and calculators. Right now on my home computer using NeoOffice, I entered "=-4^2" and got 16, so it seemed to interpret it as (-4)^2. I'll have to see what Excel on my work computer does. Using the calculator on my iPhone, I entered the following four keys: [-][4][x^2][=] and get -16 as a result. Likewise with entering it into Google or Wolfram Alpha.

@hotflashfoto 10 ай бұрын

You needn't continue down the Rabbit Hole if you don't wish to. Your evidence proves that computers need the extra steps to force them into a single result at all times. This video is a good example of teaching PEMDAS for humans, and yet our little discussion has shown that even with this, there are rules that need to be discussed. I've jokingly told people that I don't have OCD, I have CDO, which is OCD alphabetized. In this instance you can see how it might apply. I coupled the learning from my childhood with the logic from my daily job and found a small blemish that I tore into a wormhole, so to speak. But in reality, all it is is a difference in how I approached the problem from how others approached it, including the presenter himself. I would consider it a win that we've both maintained our dignity and shown others how to communicate without being rude, as we see so often.@@MadSlantedPowers

@johnplong3644 10 ай бұрын

Work from the inside out good basic problem

@bigdog3628 6 ай бұрын

[(-4 * -4 * -4) / (-4 * -4)] = -4. next we take the reciprocal of (-4) and square it which gives of 1/16. Super simple didn't need multiple choice, a calculator, or anything other than my brain and me typing into this comment.

@jeanlemire2681 3 ай бұрын

-4^3 = -64. -4^2 = 16. -64 / 16 = -4

@TerryBlush-g2p 10 ай бұрын

Somebody must be interested in this.

@slshusker 10 ай бұрын

Oops, I just died on The Oregon Trail of math forgotten rules.

@paulembleton1733 10 ай бұрын

I didn’t know about negative powers. So took a minute to check before watching. Naturally I then searched for the bit that showed whether my answer was correct 🤓 so I don’t need to watch the rest of the vid and move on to next puzzle

@kdog3908 6 ай бұрын

Just managed it in my head....Now i'm off to lie down lol. Edit: My method. I used power rules. Because you're working with the same base (-4). So, you're left with -4^1. Anything to the -2 power = 1/ anything^2. Therefore 1/-4^2 = 1/16.

@marcosofsky2605 10 ай бұрын

c)16

@Ayelmar 10 ай бұрын

At the title card, I'm going with a> 1.16.

@faithfielder9493 10 ай бұрын

I had completely forgotten the negative exponents part! I enjoyed the explanation very much.

@tomtke7351 10 ай бұрын

does -4^2 = (-4)^2 ???

@MartinHermans-dw3is 10 ай бұрын

your first expression would cause confusion to other people. a math person would write it out more clearly

@tomtke7351 10 ай бұрын

@@MartinHermans-dw3is and -4^3?

@MartinHermans-dw3is 10 ай бұрын

@@tomtke7351i changed my mind. The answer to your question is no, they are not equal

@tomtke7351 10 ай бұрын

@@MartinHermans-dw3is so "P" of PEMDAS should be employed profusely, right? it entangles my mind to encounter -4^2 now knowing it = -16 NOT 16. thus E of PEMDAS over rules what else of PEMDAS? The."-" of -4^2 is NOT S of PEMDAS. What is it?

@robertroemer4233 10 ай бұрын

Review 5:50 - 7:12 the teacher explains this in detail. Example -4^2 means positive 4 times pos 4 then take the neg of that result. The - sign is NOT attached to the 4 UNLESS the -4 is enclosed in ( ) when using powers

@bamendaoffice3482 10 ай бұрын

Thanks sir

@disneycharlton 10 ай бұрын

I will die on this hill, but -4 is a singular integer, just like positive 4. "-4" is not a compound expression of (-1 * 4). If algebra wants to separate -1 from 4, then you should write it as -(4), and that's when you use parentheses, not the reverse.

@MrSummitville 7 ай бұрын

Sorry but in mathematics ... The exponent has higher *precedence* over the *unary* negative sign. It is the negative of ... 4 raised to the 3rd power.

@gavindeane3670 7 ай бұрын

Don't die on that hill. Established convention is 100% against you and for good reason. There are similar constructs where the - symbol cannot be anything other than a negation operator, for example -(2+2)² and -x², and so for consistency the - symbol in an expression like -4² is treated as a negation operator too.

@melvynmarcus6066 10 ай бұрын

i learned something on this one

@magdalenallull3524 10 ай бұрын

Me neither

@aryusure1943 10 ай бұрын

Of course, the formula. Next time I should be able to remember it. :(

@frankcarlyle.liverpool 10 ай бұрын

It’s MATHS not math….

@stevenjohnson1143 10 ай бұрын

-4. -64÷16=-4

@oyesolaayobami6238 10 ай бұрын

A =1/16

@loloybaloloy4402 10 ай бұрын

Im naming my son Pemdas

@matikramer9648 10 ай бұрын

I had forgotten it already 🙂 though... I'm 64. Thank you

@aryusure1943 10 ай бұрын

Got it with a calculator. I forgot the rule when the exponent is a negative. Now let's see what I am missing. ;)

@محمدحمد-ه7ج3خ 10 ай бұрын

Thanks too mach

@aljjeeran 8 ай бұрын

b)1/16

@Jeanne90275 10 ай бұрын

Got it, even though I did the cubed 4 incorrectly.😊

@harrymatabal8448 10 ай бұрын

My name is Many and my answer is 1/16

@areeratasudhasirikul952 10 ай бұрын

C 16

@areeratasudhasirikul952 10 ай бұрын

1/16

@archiepuff9085 10 ай бұрын

Correct answer is (e) -4

@harrymatabal8448 10 ай бұрын

Dont blame the man for talking too much because this is his only chance to talk. At home his wife does not even allow him to even get a word in

@marknieuweboer8099 10 ай бұрын

Unnecessarily long and complicated indeed. The absolute sign means that the outcome is positive no matter what. Hence we only must calculate 4^3 / 4^2 = 4 and 4^-2 = 1/16. I did it in less than ten seconds.

@gavindeane3670 7 ай бұрын

There's no absolute value sign here. But we can immediately rule out the possibility of a negative answer, because we are calculating (something) to the power of -2, and the power of -2 can not yield a negative result.

@dawnradel9008 10 ай бұрын

@mudge40 10 ай бұрын

should have factored out the -1 and cancelled like a sensible person.

@ramesankd1604 Ай бұрын

@nicklaus8536 10 ай бұрын

I used to be told that time is important in maths. Just do the steps and we'll be less confused. Talking too much may actually confuse the students more than step by step maths.

@hqs9585 10 ай бұрын

I do have a concern with your answer. My answer is -1/16, this is why. When you have a base to a power to a power you need to solve the exponential part first before applied to the base (math algebra rule, MIT). For instance. 3^3^3 IS NOT 27 to the 3rd, (27^3), it is 3 to the 27th power. 3^27, so if you follow this well established rule then the answer is -1/16. Your comments, thanks.

@MadSlantedPowers 10 ай бұрын

I think in this case, brackets and parentheses take precedence due to order of operations. In your example, you are evaluating the exponents from top to bottom. However, if you wrote it as (3^3)^3, then the answer would be 27^3. I think all of his steps are correct.

@gavindeane3670 7 ай бұрын

You are talking about the case where an exponent is not presented as a single number, but is presented as a mathematical expression that itself includes an exponent. That is not the case here. All the exponents are simply single numbers. In the numerator the exponent is 3, and the base is 4. In the denominator the exponent is 2 and the base is -4 And for the final part of the calculation, the exponent is -2 and the base is the value of the expression ( -4³ / (-4)² ). This should also make it clear why, before even doing any calculation, we can see that -1/16 cannot be the answer. Ultimately we are calculating (something) to the power of -2, and (anything) to the power of -2 is ≥ 0.

@noobynoob6856 10 ай бұрын

I got 1/16 from the title screen

@mawavoy 10 ай бұрын

@Mr.Me.. 6 ай бұрын

I started tweaking bro, u stretch the video sm

@larrnew 10 ай бұрын

Am I supposed to remember all this….😳

@thenetsurferboy 10 ай бұрын

5 seconds in my head

@larrnew 10 ай бұрын

@@thenetsurferboy sure buddy LOL

@olivemd 10 ай бұрын

@@thenetsurferboy, I took a little longer, but it’s been a long time since I studied this. Doing math in my head sure helps as I get older.

@jimdonovan243 10 ай бұрын

Nightmare explanation. Basics are disguised under an avalanche of words.

@avirahtk6271 10 ай бұрын

Too much talk.

@danielmadden9691 10 ай бұрын

1/16

@kimbucao9291 10 ай бұрын

@stelun56 10 ай бұрын

SHOCKINGLY VERBOSE WTF DO WE NEED A CALCULATOR FOR? LOL MOST AMERICANS ARE GOING TO (NOT WILL) MESS THIS UP FOR CLARITY LMAOWRITE -4 AS (-1x4) YOU ARE GOING TO FRIGHTEN MOST PEOPLE WITH THIS SPORIOUS SPIEL

@pamelabyars3983 10 ай бұрын

B-16

@juanbonilla1006 10 ай бұрын

He talks too much and promotes his channel and himself too much. This video can easily be five minutes

@ramesankd1604 Ай бұрын

Sorryiam65yearold

@rosanne9056 10 ай бұрын

-16

@jaddwooka 10 ай бұрын

Interesting channel. I like the problems but the explanations are way... too... slow... Sorry, I understand you're targeting school age kids but I look at them as a fun refresher and I can't stand watching that long. He's driving me a bit nuts actually.