Today, we will be looking at exponents of

terms in algebra. Exponents shows how many times a number or variable

multiplies itself. Example: 4 times 4 equals 4 squared which is equal to 16 so

this is the exponent and the number here is the base. Laws of exponents. Exponents

are governed by three laws known as the laws of exponents. Please take note of

these laws they make solving problems easier. Also note that these laws only

work when the bases are the same. Law 1. The first law states that a exponent M

times a exponent N equals a exponent M plus N.

The first law is saying that when terms multiply provided their bases are the

same you can just add the exponents. Example a squared times a cubed equals a

exponent 2 plus 3 which is equal to a exponent 5. Since we’ve done multiplication ready this is familiar. Law

2 – The second law of exponents states that a exponent M divided by a exponent

N equals a exponent M minus n. For the second law we say that when terms divide

provided the bases are the same you can simply subtract the exponents. Example a

exponent 5 divided by a X minute 3 equals a exponent

minus 3 which is equal to a squared. Here you’ll see that we just

subtracted the exponents. Note that it is possible to have negative exponents.

Example a exponent 2 divided by a exponent 6 equals a exponent 2 minus 6.

This equals a exponent negative 4. Please take note of this, we will mention it

again later. Law 3 – The third law of exponents states that in (a) exponent m all exponent n is equal to a exponent MN.

We are saying that when a number with an exponent is raised to another exponent

we can simply multiply the exponents. Example (a) squared, all

cubed equals a exponent 2 by 3. This is equal to a exponent 6. Notice how we just multiplied the 2 and the 3. Important Rule derived from the laws. Let’s look at these common rules of exponents. You don’t need to memorize these. Rule 1 Any term or number exponent zero=1. Example 2 exponent 0 is 1. B exponent 0 equals 1 100 exponent 0 equals 1 this is

straightforward we’ve already seen this in lesson 1 rule 2 the next important

rule is on negative exponents negative exponent results in inverse therefore a

X minute negative M equals one over a exponent M example two

exponent negative 3 is equal to 1 over 2x minute 3 which is equal to 1 over 8

so going back to the second example of law 2 where we had a exponent negative 4

we now know we can write it as 1 over a exponent for your ability to move

between these two we’ll make the next lesson easier to understand rule 3

another important deduction is when the exponent is a fraction the denominator

of the fraction forming the exponent becomes the root of the term the rule is

a exponent 1 over M equals the M root of a example 5 exponent 1/3 equals the

cubed root of 5 notice how the 3 became the cubed root again a exponent 1 over 4

equals the fourth root of a notice how the 4 became the fourth root Effect of

exponents on negative and positive terms now let’s look at some important

information about exponents 1 any positive number or term remains positive

after an exponent operation on it example 5 squared equals positive 25 to

any negative number or term remains negative after an odd exponent operation

on it example negative 5 cubed equals negative 125 notice the exponent 3 is an

odd number hence the answer is

negative three any negative number or term becomes positive after an even

exponent operation on it example negative five squared equals positive 25

notice the exponent two is an even number please note that the parentheses

is very very very important because we are working with exponent on a negative

number I cannot over stress it without the parentheses you’ll be working with

five not the negative five try it on a calculator and notice you will get

different answers exponents on monomials now we look at how to work with

exponents on monomials example expand begin parentheses negative 2a cubed be

in parentheses all squared note you can expand and do a normal multiplication on

it but that will not be the best way the first thing you will notice is that the

term is negative and the exponent is even so the answer will be positive we

learned this earlier now we will raise the coefficient to the required exponent

the coefficient here is 2 so we will raise it to the power 2 this will give

us 4 next we will multiply the exponent of each letter by the two so we have a

exponent 3 by 2 to get a exponents then we have B exponent 1 times 2 this gives

us the exponent 2 our final answer is therefore for a exponents

be exponent two exponents on polynomials let’s move on to exponents on

polynomials example 2a plus 3b in parentheses all squared remember on the

lesson on parentheses we learned that we work with this like a single number the

best way to solve this is to expand and simplify we know that 2a plus 3b all

squared can be written as 2a plus 3b in parentheses by 2a plus 3b in parentheses

so we multiply the terms in the second parentheses by the terms and the first

so we have 2a by 2a plus 3b in parentheses plus 3b by 2a plus 3b in

parentheses now we can further expand and simplify we have 2a by 2 a to get 4a

squared then 2a by 3 B to get 6 a B next we have 3 B by 2 a to get 6 a B then we

have 3 B by 3 B to get 9b squared now we can add the similar terms we add 6 a

b-26 a B to get 12a be the final answer is therefore 4a squared plus 12 a b plus

9b squared hope this was easy everything was basically being careful

and how to multiply this question is a

typical binomial expansion we will learn an easier way to solve it but it is

still very important to learn this kind of expansion this brings us to the end

of this lesson thanks for watching encourage us to post more videos by

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Thit she right dummies

thank you so much for coming back please keep uploading because i really learned a lot from you

It's awesome

At 4:44 how is that reduced to get the one over 8? Where did the 8 come from?

Ok, this is where you lost me. Guess I know what to practice on.

Thought process for exponents 1) To Multiply or Divide exponents: Write the letter once and (+ or -) add or subtract the actual exponents together . 2) To ADD or SUBTRACT an equation that contains exponents: (+ or -) add or subtract the numbers but then write down the matching letter once and their matching exponent once, (HINT) if the letters match but the exponent doesnt they cant be added or subtracted……………………………….. They need to tell you things like : When you use "multiplication" and there are like letters that have exponents above them you write down that letter once and you "add the exponents together" . If its "division" you do the same thing except you "SUBTRACT" the exponents . There are a lot of little things like this they dont tell you out right and that is why algebra is confusing. They say these things when they are solving the problem, when you have 4 concepts you are juggling and your brain can handle any more and you get confused. If they would say ' now we are going to do this multiplication problem , be looking out for matching letters with exponents , use the letters ONCE and add their exponents together" and then you would get it. ……………………………………………………………………Now you we are "adding exponents" look for letters that match that have the same exponent too 1 X3 + 2 X3 = 3 X3 so you have 3 Xcubes, you add the numbers up but write the matching letters with matching exponents just one time. so 3 Xcube 3 X3 , if the exponenst dont match then nothing changes 1 X2 + 2 X3 ………………………………………… If you are "subtracting" its the same but you subtract the numbers instead of adding them 1 X3 – 2 X3 = 1X or just X . …………………………………………………………………………………lets make this even simpler if you Multiply or Divide exponents write the letter once and add or subtract the exponents . If you add or subtract exponents add or subtract the numbers and write down the matching letter once and the matching exponent once. ……………………………………………………….. Simpler yet whne it comes to exponents : if you see a a multiplication or division symbol look fore macthing letters , write that letter down and add or subtract the exponents… if you see a plus or minus sign look for macthing letters with matching exponenst and write it down , then add or subtract the numbers. Mult /Div : match letters add/sub exponents. Add/Sub: match letters and exponents then add/sub the numbers. Multiplication: add exponents DIVISION: Subtract exponents Addition: add the numbers Subtraction: Subtract then letters and exponents must match

6:53 I don't understand this low ? Please any help

Edit : I understand know 😘

love math. excellent videos

Thank you😊

Very interesting

I will never understand this

thx a lot I learn a lot with the help how this video

Thank youuuuu 😊

Im really bad at math and algebra worries me alot so when i came across your channel , you made me love and understand math more! Thank you for helping. I dont think i will struggle in school with my math. Also another question , will you post more of these kinds of algebra parts like part 4??

There's a reason why I hate Math because I don't understand it but I'm learning a lot from your videos, thank you. I'm going to keep watching until I get it.

I see what you did there on the last one. I remember solving that in HS using FOIL.

Thank y’all for helping me really Appreciate what are y’all doing for free

Parts 1 and 2 were like "ok, I get it"

Part 3 was like " wait wtf *rewind*"

Dummies

says its made in 2018 but the 2004 software and graphics says something else.

At 4:42 how did it became 1/8 ??? Help 😭😂

Could you explain the equation at 9:41 a little more?

I'm wondering why you can't say

2a*2a=4a²

3b*3b=9b²

4a²*9b²

Also, where does the 2a and 3b outside the parentheses come from when you work this out?

2a(2a+3b) * 3b(2a+3b)

Can someone please explain to me how the answer is -125 at 6:35? I'm really lost…

Thank you so much for these videos! They are the best I have found at explaining algebra!

4:30 why does it have to be in fraction form?

Part 1 n Part 2 was okay yes I got this BUT part 3. Need more of an explanation. I’m so lost.

Is this video considered to be pre-algebra or algebra?

Im. Poor at math but i have never forgotten this method of solving by using foil, of course the long way… I still have to learn the short way…

Part 4 pleaeeeeeee

Thank god I found your channel!!! I finally mastered part 1-3 and I'll be ready next time my math teacher( that gives quizzes and doesn't even teach) gives us another quiz

p.1=and

p.2=I

p.3=OOP.

Can’t wait for algebra now. F me

Thanks you r the best!!!!

Great teaching skills mam,very useful for me.i am from India 🇮🇳

Thank u mam….

Thanks so much for the most needed help. I think a mini quiz at the end would be helpful as well. As a recap and to find the areas where ppl need more help in and to make it sink in more. Thanks again!

Been watching bunch of algebra videos and this is the first one I've seen that mentioned the exponent rule of even or odd numbers affecting the answer….ugh Soo much to learn still