03 - Negative Exponents & Powers of Zero (Laws of Exponents), Part 1

View more at www.MathTutorDVD.com.
In this lesson, you will learn how to simplify expressions that involve negative exponents in algebra. First, we will show what a negative exponent is and how it relates to an exponent of zero (power of zero).
Negative exponents represent small numbers, while positive exponents represent large numbers. We will simplify numerous expressions with zero and negative exponents in preparation for solving equations with a negative exponent.

Пікірлер: 290

  • @ojobomary7
    @ojobomary74 жыл бұрын

    Why are we not getting teachers like you in school these days... Thank you so much. This was crystal clear.

  • @Fuindion

    @Fuindion

    4 жыл бұрын

    Not.

  • @jayurban4313

    @jayurban4313

    3 жыл бұрын

    Was

  • @ReddogOfficial

    @ReddogOfficial

    3 жыл бұрын

    Ikr 🤣

  • @buffplums

    @buffplums

    3 жыл бұрын

    This has always been the case. For me maths teachers always just presumed that everyone understood I teach maths now and I often get accused of going too deep but all I’m doing is trying to make sure that the small minority of my students understand

  • @victorlonge7151

    @victorlonge7151

    2 жыл бұрын

    That true

  • @Obsidian_Iris_
    @Obsidian_Iris_2 жыл бұрын

    You’re an excellent instructor. Thank you so much! I’m not a student; I’m an adult. Math was always my favorite subject, particularly algebra. Math was the one subject I never had to study outside the classroom. They way I saw it, when we learned a different topic it was a matter of learning a formula and our homework was simply plugging different numbers (in a variety of forms0 into that one formula. It was as easy as breathing air. I loved the way we learned a simple formula and constantly build on it to make more complex formulas. I was never really able to use or understand, shortcuts; I needed to know exactly why something worked, not just how to do it. I’m thrilled that you explained both and that I was able to understand them. I remember in algebra class, I was the only one who knew a number with an exponent of 0 is 1 but I didn’t know why until today. At the time, I had read it somewhere but the book didn’t explain why. Like many people, had my education interrupted by chronic illness. My biggest regret in life is not having the opportunity to advance in my s education to my fullest potential. Ironically enough, I was able to teach myself enough (from library books; the Internet didn’t exist) to win a full scholarship to college but was derailed by illness again again in my third year. To you students out there, please don’t take your education for granted. Do the best you can in every subject, even if you don’t feel it will be relevant to your adult life. If there’s a subject or subjects you particularly like, learn all you can, above what’s expected. How far you progress and how well you do in high school and college/trade school will profoundly affect the rest of your life. Do not get into the trap of taking a dead end job right out of school, no matter how well you think it pays. What you do or don’t do in early adulthood will have a huge impact on your quality of life later on. That being said, doing what you love is what’s most important. Don’t plan to become an accountant, lawyer, doctor, etc. because of the potential salary. If you love drawing and want a career based on it, it’s absolutely possible to live well with a career in art. There are a multitude of ways to do so both as an entrepreneur and within a company. You will need to plan accordingly and find resources for guidance. Even with my chronic illnesses, if I had had any emotional support and practical, knowledgeable guidance, I could have continued my education and reached my goals. If you don’t have any support from your family, look for information and guidance, even if it’s via Internet.

  • @vishnusathasivanjoghee

    @vishnusathasivanjoghee

    2 жыл бұрын

    Excellent elucidation

  • @c4rrot508

    @c4rrot508

    2 жыл бұрын

    I almost cry because when I was in 5th grade (currently a incoming sophomore in highschool) I lost interest in school, through middle school I didn't pay attention, turn in test without nothing answered, I just went to school and mess around I didn't learn anything and I regret so much that I wished I could of taken seriously and I wouldn't be here trying to catch up all this four years of school learning in summer break.. I believe in myself that is still isn't late and I could make a life staring now especially because I am young and I can't be throwing my life away like that easily , also my mother doesn't have faith in me and I know I been unhelpful (she says only true people who want to be a doctor were born do for it.. But believe I will find later on my career dream , I honestly have zero goals in life and career plans but I pray that I find myself) Thank you for motivating me more!

  • @emjaydark2811

    @emjaydark2811

    2 ай бұрын

    @@c4rrot508You may become a math teacher.

  • @mjneuf_
    @mjneuf_4 ай бұрын

    My math teacher was great, but I had really bad foundations. And more than that, I was always asking why. Like a toddler: why, why, why? This video explained the actual reasoning behind the rules and I could not be more grateful! I’m watching the whole series, thank you so much.

  • @bangtansouleiam
    @bangtansouleiam2 жыл бұрын

    i'm a 9th grader here in our country and to be honest, i've never seen a math teacher or even a teacher like you in my experience, so far and i hope you're like the teachers here because you explain math problems like a crystal clear 😊

  • @josenavarrete8566
    @josenavarrete85663 жыл бұрын

    This is really helpful! Especially when taking higher math courses like calculus1, 2 and 3.

  • @Hypatia350
    @Hypatia3508 ай бұрын

    You're the best teacher I've found on YT. I'm a 48 year old social science teacher and I've suddenly become interested in math!

  • @sarmi6394
    @sarmi63943 жыл бұрын

    Its funny that the best teacher i have is on KZread...no matter the subject, ur explanations are really good and let people understand math better. 🙏

  • @nm1978
    @nm19782 жыл бұрын

    My God, you are the best greatest teacher on earth, I don't know if there is or not anyone else that I know that teaches so clearly in detail, you should be an example to the entire world's education systems. The entire world education systems must be changed, this is how everything should be taught , instead of long boring lectures, or reading books that are so hard just to understand what they are trying to tell you, because the way books are written is very official language which I abhor, a simple concept that can take one minute to understand takes hours, because the way these evil books are written , the concepts of science, math and everything else are not hard to learn and are actually fun to learn, if it wasn't for these official languages that are used in all books, I am so sick and tired of them. This is how everything should be taught in all schools. Simple, fun and clear. They should learn from you, you are the best and made a big difference in my life, truly American teachers are the best too at teaching. But offcourse your ways of teaching makes it the 👌 best.

  • @casara555
    @casara555 Жыл бұрын

    You are getting me through school. I haven't had a teacher yet that explains these things to me like you do. I don't know why this is, but you just know how to explain it to me in a way that I can understand. I truly appreciate you, you helped me actually like math and to not be scared of it.

  • @jessicabattle5732
    @jessicabattle57322 жыл бұрын

    You make me feel like I can accomplish anything. Thank you, truly. From the bottom of my heart!

  • @MathAndScience

    @MathAndScience

    2 жыл бұрын

    I think this might be my favorite comment of the week! It really is what I’m striving to achieve, I want you to feel like you can accomplish anything and then nothing stands in your way toward success. I used to be that student in class I didn’t understand anything so I know exactly what it feels like to not get it and I really hope that through my lessons I can help more students feel that they really CAN get it.

  • @elhamkhan8796

    @elhamkhan8796

    2 жыл бұрын

    @@MathAndScience man i love your teaching so much

  • @26rey01rc93

    @26rey01rc93

    Жыл бұрын

    @@MathAndScience like I said you're so amazing a blessing in disguise, no teacher will reveal what you're doing, so smooth straight to the point, such a lovely Man a "gift" from God, to be honest, now many Students will love you, this is the most Hated subject on PLanet cause Teacher not sharing their Knowledge. Really love your Passion of Teaching, the Hardship and Efforts you made, what can I say more, thanks forever, Sir Blessed.

  • @kubakakauko
    @kubakakauko4 жыл бұрын

    Perfect, Thank you! I love your teaching style.

  • @fikilekhanyile8531

    @fikilekhanyile8531

    2 жыл бұрын

    Thank you for your time making me understand Mathematics better

  • @225rip
    @225rip3 жыл бұрын

    Thanks for going the extra mile to explain why.

  • @lorrainepennell1838
    @lorrainepennell18382 жыл бұрын

    I love this guy. He explains concepts in a way that anyone can understand. I have learning issues and these videos help me so much!

  • @bermarte
    @bermarte3 жыл бұрын

    I use these explanations to understand other explanations on the same subject. It is so rare to find a teacher like you.

  • @annettevonbrughan7874
    @annettevonbrughan78742 жыл бұрын

    I haven't done math since 1968 and struggled much. The way you teach makes math concepts so clear and understandable. THANK YOU

  • @TheKonzue11
    @TheKonzue113 жыл бұрын

    I just want to say I love you 😭😭 and thank you so much

  • @vivekbalachandran9414
    @vivekbalachandran94143 жыл бұрын

    I was wondering to recall all the maths to improve DataStructure and Algorithm concepts, this video made me totally relaxed in this topic. Using this, I can crack almost all the problems of exponent in programming. Thanks.

  • @nakimajoseph8824
    @nakimajoseph88243 жыл бұрын

    OMGOSH SIR THANK YOU SO MUCH 😭😭😭 I WAS LITERALLY STRUGGLING WITH THIS TOPIC

  • @user-tj6ow5sg8p
    @user-tj6ow5sg8p3 жыл бұрын

    BA Student in China but kinda watching your videos to recap some of the basics and it was so awesome. Thanks a lot. 感谢!!!

  • @MathAndScience

    @MathAndScience

    3 жыл бұрын

    You are very welcome!

  • @widgeonslayer
    @widgeonslayer4 жыл бұрын

    I am studying in preparation for returning to college. Amazing how much you can forget in 11 years. I am very thankful that you explain why you are doing something. Not just saying to do it. I cant learn that way.

  • @robertkay9349

    @robertkay9349

    4 жыл бұрын

    widgeonslayer, I. too, am taking college algebra after a long absence from school. In my experience, it's amazing what you can forget in 40 years.

  • @widgeonslayer

    @widgeonslayer

    4 жыл бұрын

    @@robertkay9349 going to be interesting for sure. What program?

  • @robertkay9349

    @robertkay9349

    4 жыл бұрын

    widgeonslayer I’m in my last few classes for associates of business then will transfer to UNLV for a bachelors in either marketing or real estate.

  • @widgeonslayer

    @widgeonslayer

    4 жыл бұрын

    @@robertkay9349 sounds like a good program. I'm going to the university of Montana for welding. It's a 2 year program and will graduate with an associate's. From there I can either go straight to work or further it into a bachelor's.

  • @robertkay9349

    @robertkay9349

    4 жыл бұрын

    widgeonslayer good luck with that. There’s a lot you can do if you piggy back a bachelors off some experience as a welder.

  • @sarahhanawalt2036
    @sarahhanawalt20363 жыл бұрын

    Thank you for explaining Powers of Zero. It helps to make sense of math. It also builds conceptual learning which is missing in America's School System.

  • @mjcard
    @mjcard3 жыл бұрын

    So exquisite, clear, brilliant pedagogy!!!! Thank you, thank you!

  • @Acadia26
    @Acadia263 жыл бұрын

    In my experience, the more steps you take to work something out the more the chance of making a mistake. It's best to learn that any fraction raised to a negative power is the reciprocal raised to the same power but positive. For example (3/5) to the power of -3 is equal to (5/3) to the power of 3. This way, you get rid of double stacks of fractions, working them faster and having fewer steps to make mistakes in.

  • @Obsidian_Iris_

    @Obsidian_Iris_

    2 жыл бұрын

    Not so. As he said, it’s best to know why something works, not just how to do it, if only for instances when you come across an equation where the shortcut doesn’t work or more importantly, you’re given a scenario that requires you to set up the equation yourself based on the information requested. This is the case in many standardized tests and entrance exams for many institutions and companies. In such a case you need to understand the theory. Not just know a method. As he said, there are often many ways to solve a problem. If you understand the theory, you can determine the best way to solve the problem, which may or may not allow a shortcut. It’s best to know why before you learn how and it’s not as if he said not to ever use shortcuts,only to know the theory first. There’s another KZread channel, MindYourDecisions, that illustrates this well. He provides mathematical puzzles many of which look deceptively simple. Many require you to set up the equation which means you have to know why, not just how.

  • @dominiquez5643
    @dominiquez56432 жыл бұрын

    Wooooow! Blew me away! Thank you for your time, experience and for leveling down to what I needed! Amazing explanation !!

  • @bongzkietanglao6706
    @bongzkietanglao67064 жыл бұрын

    great explanation! Really helps *liked* But what if the exponent is a fraction and is a negative multiplied by a negative? Ex.(a^2/3)^-3

  • @sakikogookheng
    @sakikogookheng Жыл бұрын

    Fantastic video as usually!. Building on what you said on anything (bar 0) raised to the 0th power being 1, Khan academy did a good video on it, expanding on what that could mean. He said that you could look at the exponent as how many times you need to multiply 1 by that base power. So 2^3 could be seen as 1 needing to be multiplied by 2 3 times, since you need to multiply 1 by 2 3 times to get your answer; that'd be 1 x 2 x 2 x 2, so 8. So for 2^0, the amount of times you need to multiply 1 by 2 to get your answer would be not at all, so the calculation would just be summed to 1, since you'd need to multiply 2 by 1 zero times. 2^0 = 1 2^1 = 1 x 2 2^2 = 1 x 2 x 2 2^3 = 1 x 2 x 2 x 2 I haven't done the explanation justice, so if anyone's still struggling, Google "The 0 & 1st power - Khan Academy".

  • @ricardolucas1624
    @ricardolucas1624 Жыл бұрын

    You're terrific teacher. The way you explain everything is precise . Thank you.

  • @nastassjapamelabenjamin4915
    @nastassjapamelabenjamin49152 жыл бұрын

    I wish I could give you a 1000 likes, I am loving your teaching methods. Thank you for taking your time to do this for us, you a great teacher. 📚🔝✔💫

  • @dansinn
    @dansinn3 жыл бұрын

    Amazing as always, you are one of the most best teacher ever

  • @finalcombat9036
    @finalcombat90364 жыл бұрын

    Thank you so much I’ve been relearning math and this has been helpful

  • @sheilajogoo5732
    @sheilajogoo57324 жыл бұрын

    Love your explanations. So clear

  • @SabinaCovarrubiasComposer
    @SabinaCovarrubiasComposer4 жыл бұрын

    Thanks for explaining WHY. So I don't have to swallow a nonsense formula :)

  • @honiaumed6616
    @honiaumed66163 жыл бұрын

    I couldn't understand from my teacher who always brags how she always was the best in her school days I came to you,thank you

  • @rolandvan236
    @rolandvan2363 жыл бұрын

    Thank you for showing where the math comes from.

  • @nickaguirre6317
    @nickaguirre63173 жыл бұрын

    Great video. Thank you for the explanation!

  • @itseby3642
    @itseby36423 жыл бұрын

    Thank you for explaining different ways to the answer!! ❤️

  • @rickdeckard2622
    @rickdeckard26223 жыл бұрын

    I love these explanations!

  • @Skootzbot
    @Skootzbot2 жыл бұрын

    Bro your teaching style is fire. Been a long time for me I really appreciate you taking the time to break this down

  • @MathAndScience

    @MathAndScience

    2 жыл бұрын

    Thank you so much!

  • @jackdeanda2311
    @jackdeanda23116 ай бұрын

    Appreciate the visual of the negative exponents , you're amazing!

  • @danielkaigatyielliah5463
    @danielkaigatyielliah54632 жыл бұрын

    It's the first time to get teacher, teaching like 💕 u Thanks for your experience

  • @_outfit_ideas_
    @_outfit_ideas_2 жыл бұрын

    This why technic is so useful for to feel and visualize maths. Thank you so much 🥰😇😇😇😇

  • @LieketsengMolekane-ys4ub
    @LieketsengMolekane-ys4ub Жыл бұрын

    The best teacher in the world..I hated maths but you made me think otherwise so thank you so much🙏

  • @ndubuisiaguihe340
    @ndubuisiaguihe340 Жыл бұрын

    You are a good teacher. I think this what you can do best. You are a genius.

  • @therealtreasure7591
    @therealtreasure75912 жыл бұрын

    Sir, your explanation is very excellent. Thanks a lot.

  • @karellejayson5851
    @karellejayson58513 жыл бұрын

    Do you have an explanation video about addition and subtraction of numbers with negative exponents?

  • @26rey01rc93
    @26rey01rc93 Жыл бұрын

    You're so amazing Sir Jason , you uncover the hidden secret of this business, thanks a lot for revealing to us that has mathphobia complication for a long time, hopefully the new generation will enjoy math cause of your teaching method your so kind you share what you experience before and discover, God bless you more Sir, take care.

  • @sarahmapes9955
    @sarahmapes9955 Жыл бұрын

    Thank you sooo much!! Very throughly explained and made easy!! 🙏

  • @bombayhangerb438
    @bombayhangerb438 Жыл бұрын

    My search, for a perfect understanding on negative exponents ends here.. Thank you so much 👍🙏

  • @ShaktunTala-lu4hj

    @ShaktunTala-lu4hj

    4 ай бұрын

    You are best

  • @jordeahingpit9416
    @jordeahingpit9416 Жыл бұрын

    Thank you for clarifying to us about this rule.. I learned a lot.

  • @naderhumood1199
    @naderhumood1199 Жыл бұрын

    Sir, you really did tremendously well. Thank you v much indeed.

  • @feliciabruton4054
    @feliciabruton405411 ай бұрын

    You are an exceptional teacher. Thank you for sharing.

  • @DarkMoonlightAngel
    @DarkMoonlightAngel3 жыл бұрын

    Very well expounded. Thank you so much. I wish you are my mentor.

  • @Pathrisha
    @Pathrisha2 жыл бұрын

    This guy is actually better than my math teacher- and I understand it more than my teacher. Like literally Everytime she explains something, it's always confusing. But this guy is like having a stroll at the park when his explaining. It's so clear. Like, why don't we get teachers like you??!?!?!

  • @MathAndScience

    @MathAndScience

    2 жыл бұрын

    Awww thank you so much!

  • @staciehernandon7115
    @staciehernandon71154 жыл бұрын

    Great video and explanation

  • @pawarlaxman2574
    @pawarlaxman25742 жыл бұрын

    So good teaching as correct and perfect nature of teacher 🙏🙏

  • @NJASpace
    @NJASpace Жыл бұрын

    Thank you soo much! Your teaching helped me ace my math test!

  • @gtrendsceaccount9870
    @gtrendsceaccount9870 Жыл бұрын

    Fantastic explanations. You laid the beauty of math

  • @MathAndScience

    @MathAndScience

    Жыл бұрын

    Glad it was helpful!

  • @darlenescott2162
    @darlenescott21622 жыл бұрын

    We need teachers like this

  • @meganpadayachee6791
    @meganpadayachee67912 жыл бұрын

    You are a great teacher. Thank you.

  • @magedx7059
    @magedx70594 жыл бұрын

    Great teacher!

  • @Carlos-qz7ul
    @Carlos-qz7ul Жыл бұрын

    Incredible teacher ! ❤

  • @sandilepenwell8598
    @sandilepenwell85982 жыл бұрын

    You're the best, you just do things easier

  • @akshudhage13
    @akshudhage132 жыл бұрын

    It is useful video this sir teaching can make our maths more better and lit bit English language also ☺️

  • @princesingh-it3du
    @princesingh-it3du4 жыл бұрын

    GREAT EXPLANATION !!!

  • @luyombojonathan7715
    @luyombojonathan77152 жыл бұрын

    Great content sir !! Cheers

  • @His-Soldier
    @His-Soldier2 жыл бұрын

    Rule 1: 09:11 Rule 2: 12:18 Shortcut for fractions with negative powers in the denominator and numerator: 30:41

  • @-MissSiri-

    @-MissSiri-

    Жыл бұрын

    Thanks!

  • @edsonharawa167
    @edsonharawa167 Жыл бұрын

    You are a good lecturer sir.more grace

  • @tubeyou988
    @tubeyou9883 жыл бұрын

    thank you sir! its a big help for me

  • @latoniajones8304
    @latoniajones83043 жыл бұрын

    this really helped me thank you

  • @armando9740
    @armando9740 Жыл бұрын

    You can see that n^0 is 1 even before seeing the proof just by remembering that anything multiplied by 1 is equal to itself. What this rule clues us into is that arithmetic is the science of counting by one, everything is based on increasing or decreasing by increments of one, or fractions of one. All the tricks they teach us, like the reciprocal, cross multiplying, moving negative signs of fractions, are just clever applications of fractional ones. The word "unit" is related to the word "unity". For example, the number 8 is really 8(1) or (8x1)/1, eight ones. So 8^3 is 8x8x8x1, you can see that if you remove three 8's you're left with one as 8^0, because you got rid of all the eights. 8^1 is eight times bigger than one, then 8^-1 or 1/(1x8) is 8 times smaller, and 8 only exists as a comparison or ratio to 1, as any number is some quantity related to one. You can see that you are just manipulating the unit one, counting with one, then either multiplying it by some number over and over, or dividing it by some number over and over. The negative exponent is an example of extending the meaning of a preexisting symbol, since division is related to subtraction. Edit: Also forgot to mention, negative just mean opposite, so in the case of 8/1 vs 1/8 the opposite of eight times bigger is eight times smaller, therefore 8^1 vs 8^-1.

  • @lipikananda3942
    @lipikananda3942 Жыл бұрын

    I love your teaching .thank you sir.

  • @extraterrestrialcontent
    @extraterrestrialcontent4 жыл бұрын

    Thank you soo much bless this video

  • @marytredinnick3366
    @marytredinnick3366 Жыл бұрын

    You're very good at explaining this

  • @harrisongideon3993
    @harrisongideon39932 жыл бұрын

    Thank you. This helped so much.

  • @chipia8451
    @chipia84512 жыл бұрын

    Thank you & God bless you

  • @billreed3265
    @billreed3265 Жыл бұрын

    This is a great teacher

  • @FelipedeSouza
    @FelipedeSouza4 жыл бұрын

    Thank you!

  • @samanthacollins7666
    @samanthacollins76662 жыл бұрын

    With you negative exponents are not clear to me because I am autistic and you don't know about autism but with Mrs. Durr I understand negative exponents but with only Mrs. Durr. I really like you Mrs. Durr 👏👏👏👏😇😇😇😇😇🤩🤩🤩🤩❤🤟🤟🤩🤩😁😁😁😁😁😁

  • @Emmanuel-wk8wv
    @Emmanuel-wk8wv11 ай бұрын

    I love your teaching

  • @sofilatif4796
    @sofilatif47963 жыл бұрын

    Thanks It's good style to teach students Well done 🙄

  • @edwardreichard3852
    @edwardreichard38522 жыл бұрын

    Can you write this promblem out for me please and explain? 1/2+1/3+1/5 to minus1. I used the common denominator to get.9677. The neg exponent-1, does it mean flip the fraction over

  • @oscarfucanan4618
    @oscarfucanan46183 жыл бұрын

    Nice lesson instruction...sir.. God bless

  • @ShaktunTala-lu4hj
    @ShaktunTala-lu4hj4 ай бұрын

    Best teacher

  • @josephkim1829
    @josephkim1829 Жыл бұрын

    our school needs to hire this guy

  • @JB-tc2ug
    @JB-tc2ug4 жыл бұрын

    Great detailed video

  • @MathAndScience

    @MathAndScience

    4 жыл бұрын

    Thanks so much!

  • @fanchatakudzwakaseke6066
    @fanchatakudzwakaseke60662 жыл бұрын

    very clear thank you

  • @Eagle01900
    @Eagle019009 ай бұрын

    Thanks million, teacher. You're great.

  • @MathAndScience

    @MathAndScience

    9 ай бұрын

    Thank you! 😃

  • @kyra9032
    @kyra9032 Жыл бұрын

    how do you do -6(2/3)2 i cant find any videos on it

  • @gilbertdatun3275
    @gilbertdatun32753 жыл бұрын

    Well-explained😍😍

  • @karan_karan_karan
    @karan_karan_karan3 жыл бұрын

    this was good! thank u!!!!!!!!

  • @Lacombe-dk6eo
    @Lacombe-dk6eo2 жыл бұрын

    Thank you so much.

  • @buhlendlovu9224
    @buhlendlovu92243 жыл бұрын

    thank you so much this helped

  • @katherynvalle5888
    @katherynvalle58882 жыл бұрын

    Thank you sir ❤

  • @kevinjavia-zr2mq
    @kevinjavia-zr2mq Жыл бұрын

    Thanks it much clearer than my teacher explains

  • @narayananarayanakumar1466
    @narayananarayanakumar14662 жыл бұрын

    Sir ur explainatiin sir excellent💯👍👏 in my life where I saw the teachers

  • @emjaydark2811
    @emjaydark28112 ай бұрын

    Thank you again.

  • @juanimel_b1
    @juanimel_b12 ай бұрын

    you are a hero

  • @brentfairley5156
    @brentfairley5156 Жыл бұрын

    Great video

  • @tahirlatif2563
    @tahirlatif25632 жыл бұрын

    Impressive. Respect from Pakistan 🇵🇰

  • @izzvenom6013
    @izzvenom60133 жыл бұрын

    very good explanation