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

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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.

[@ojobomary7]

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Not.

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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

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[@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.

[@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.

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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!

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[@Acadia26]

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_]

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[@sarahhanawalt2036]

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.

[@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".

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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.

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[@His-Soldier]

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

[@-MissSiri-]

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

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[@armando9740]

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.

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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

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