GED Math: Intro to Exponents Virtual Class Video 0.2 

Practice this skill at www.lightandsaltlearning.org/0-math-101/intro-to-exponents

You are literally the best teacher I have ever experienced and I am 35 years old. I have never been able to understand most math teachers cause it takes skill to teach me math lol. But I am so very excited to have found you and I can't express that enough, so thank you very much! This is the final test I need to pass cause I got a 143 on the first one and did a retake and got a 139 so very depressing and I gave up and ive let 1 1/2 yrs go by and now I have decided to start from scratch so I can pass this sucker I am so disappointed in myself that I have given up untl now but I believe i will do great now I found your videos and hope your able to get the rest up soon so I can pass this test. Thanks so much with all my heart you rock, great personality girl!

My notes/summary *Exponents / power* exponents are a shortcut way to write repeated multiplication 7(5) = 7 + 7 + 7 + 7 + 7 7⁵ = 7 ⋅ 7 ⋅ 7 ⋅ 7 ⋅ 7 the number being multiplied by itself is the base (7) the number of times the base is multiplying by itself is the exponent (⁵) exponential form is written as a base and an exponent (7⁵) expanded form or factored form (meaning multiplication) is written as a multiplication expression (7 ⋅ 7 ⋅ 7 ⋅ 7 ⋅ 7) *Examples* 1⁵ in expanded form is 1 ⋅ 1 ⋅ 1 ⋅ 1 ⋅ 1 2³ in factored form is 2 ⋅ 2 ⋅ 2 5 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 in exponential form is 5⁶ x⁸ in expanded form can be written as x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x, (x)(x)(x)(x)(x)(x)(x)(x), or xxxxxxxx it doesn't matter what x is *4 special exponents* 0 and 1 are special because of their behavior ⁰: anything to the 0th power is 1 (not 0!) 7⁰ = 1 2934⁰ = 1 (2/3)⁰ = 1 x⁰ = 1 ¹: the base doesn't change 7¹ = 7, like how 7 x 1 and 7/1 are both still 7 2934¹ = 2934 (2/3)¹ = 2/3 x¹ = x 2 and 3 are special because they're called different things ²: square (squaring a number) 7² can be called "7 to the second power" or "7 squared" ² means squared like how a square is 2D ³: cube (cubing a number) 7³ can be called "7 to the third power" or "7 cubed" ³ means cubed like how a cube is 3D *Questions that ask for answers* a question asking for the answer will say "simplify" or "evaluate," or put an equal sign (=) or indicate one in words ("what is") 1. simplify 2³ the answer is 8 exponents involve multiplication, but 2³ is not the same as 2 ⋅ 3 to make it easier to understand, write the expression in expanded form before answering (2 ⋅ 2 ⋅ 2) 2. evaluate (17/3)¹ the answer is 17/3 because x¹ keeps the number as it is you don't need to simplify the fraction if it's been reduced to lowest terms 2b. evaluate (16/12)¹ the answer is 4/3 because 16/12 is not reduced to lowest terms 3. z⁰ = the answer is 1 because ⁰ always makes the number 1 4. what is five cubed? the answer is 125. "five cubed is 125" is the same thing as "5³ = 125" everything so far would be on the non-calculator section of the GED *Examples* 1. simplify 2⁵(2³). express your answer in exponential form rewrite the expression in expanded form. start with the first piece. 2⁵ = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 parentheses means 2³ is being multiplied, and 2³ = 2 ⋅ 2 ⋅ 2, so this is 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 the only number is being repeatedly multiplied. 2 is multiplied by itself 8 times, so 2⁵(2³) simplified in exponential form is 2⁸ 2. 3⁸/3⁵ the fraction bar signifies division rewrite the top and bottom numbers in expanded form. 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3/3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 having the same number at the top and bottom of a fraction cancels them out. there are five 3s at the bottom and top, so the groups of 5 can be scratched out that leaves 3 ⋅ 3 ⋅ 3 (over nothing), so the answer is 3³ 3. x⁵/x⁴ this can be rewritten in expanded form as xxxxx/xxxx. four xs cancel out, so the answer is x the answer is not x¹ because, while true, it's not the simplest form 4. 5³/5³ 3 - 3 = 0, so 5³/5³ = 5⁰ the 0th power is always equal to 1, so 5³/5³ = 1 this is also proven because fractions with the same numerator and denominator equal 1 5. (2³)⁴ this is not a multiplication problem. this is 2 cubed to the 4th power 2³ = 2 ⋅ 2 ⋅ 2, and the parentheses around it means that entire thing is to the 4th power, so it's (2 ⋅ 2 ⋅ 2)⁴ everything in parentheses is multiplied by itself 4 times, which can be written as (2 ⋅ 2 ⋅ 2)(2 ⋅ 2 ⋅ 2)(2 ⋅ 2 ⋅ 2)(2 ⋅ 2 ⋅ 2) or 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 that's twelve 2s, so the answer is 2¹² *Rules* (shortcuts) product rule: when multiplying like bases, add the exponents (example 1) quotient rule: when dividing like bases, subtract the exponents (examples 2, 3, and 4) power rule: when raising an exponential expression to another power, multiply the exponents (example 5)

You make math less terrifying. Thank you for being such a badass teacher.❤️

You can tell how good of a mathematician she is just by how easily she explains these concepts to people who are new to it. You gotta be REALLY smart to make someone like me understand it this fast, thank you so much!

This video is amazing!

Awesome and brilliant way of teaching! I can understand your teaching in a practical and easy way. I'm planning to do my GED in 2 months! Keep up the good work, and God bless you!

Wow this is the best thing I’ve ever ran across. You explain so well

So glad I found your channel your a brilliant teacher!

I never learned exponenets, very informative.

Great video

Thank you teacher Kate !😊

very helpful,thanks

Love her methods

the answer to 7 times its self 5 times is16807 😵‍💫😵‍💫😵‍💫