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

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.

[mjneuf_]

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.

[ojobomary]

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

[Hypatia]

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!

[Obsidian_Iris_]

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.

[nm]

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.

[mizbangtan]

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 😊

[josenavarrete]

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

[sarmi]

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

[cas-g]

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.

[rip]

Thanks for going the extra mile to explain why.

[萨萨图雷]

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！！！

[jessicabattle]

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

[kubakakauko]

Perfect, Thank you! I love your teaching style.

[annettevonbrughan]

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

[TheKonzue]

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

[widgeonslayer]

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.

[sakikogookheng]

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".

[bermarte]

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

[honiaumed]

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

[nakimajoseph]

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