Division and Exponents

Division 

Division of whole numbers is basically for any whole numbers r and s, w doesnt equal 0, the quotient of r divided by s, written r divided is the whole K, if it exists such that r =s x k


Example of this would be:

18 divided by 3 =  6    -------------   6 times by 3 = 18

24 divided by 6 = 4    -------------    6 times by 4 = 24

35 divided by 5 = 7   -------------    5 times by 7 = 35
              
        *this is called  inverse operation, it means to undo eachother
          so to undo dividing is to multiply.
Another way to work out division would be to make a picture.

If i had 15 basketballs and had 3 groups to divide the 15 balls into, how many balls would be in each group?
0 = basketball
Group 1-- o o o o o
Group 2-- o o o o o
Group 3-- o o o o o
What you need to do is put one basketball in each group so you have an the same amount or basketballs in each group.
Ask yourself how many groups are you supposed to have? answer is 3
How many balls are in each group? 5
this would be 3 times 5 = 15

You can also ask yourself how many basketballs do you have total? answer is 15
How many groups do you need? 3
How many times does 3 go into 15? 3,6,9,12,15.. so the answer would be 5.

Hopefully that helps you understand the concept of inverse operations.
                                 Exponents 

Image from
My absolute favorite!
there are basic rules that are needed to be followed for exponents.
Exponentiation- means for any number B and any whole number N with B and N not both zero.
Basically this means that if you have B raised to N that it will = B times B times  times B
making B occur N times.
where B is called the base and N is called the exponent.
4 raised to the 0 power is equal to 0.. because 4 times 0= 0
4 raised to the 1 power is equal to 1.. because 4 times 1 =1
4 raised to the 2nd power is equal to 16 .. because 4 times 4= 16
What is 3 raised to the 2nd power?

9 -- because 3 times 3=9

now if you had 3 raised to the 10th power it would look like .. 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3-- there are ten 3's being multiplied together. There are 10 of them there because 3 was being raise to the 10th power.

If you have 2 raised to the 4th power being multiplied by 2 raised to the 3rd power.. what would you do to the exponents?
would you Add them?
                 Subtract them?
        or      Multiply them?

you would add them so it would be 2 raided to the 7th power. it would look like 2 x 2 x 2 x 2 x 2 x 2 x 2 --
seven 2's are being multiplied together.
The only time where you will be adding exponents is if the bases being multiplied are the same. 

If you are dividing you would do the same exact thing just subtract the exponents.
hopefully this video will help you see, because it was hard for me to explain since i cant raise exponents on my computer