* LAWS OF EXPONENTS
** RECAP
*** BASE
This is the number to be multiplied to itself

*** EXPONENT
this tells  us the nuumber of  times that the base  will be
used as a factor

*** POWER
Collective term for base and exponent
** CONTENT
*** PRODUCT RULE
same  base but  add  the exponents,  just  add the  goddamn
exponents, the base means nothing to you here.

            FORMULA: a^m . a^n = a^m+n
            EXAMPLE: 3^5 . 3^7 = 3^7+5 (3^12)

if its different bases, you cant add them, you need to copy
the two different bases, thex  product rule only applies in
situations where the base is the same

Also, if they're variables, dont  put the sign, but they're
constants, please do so:

           a^1 . b^1 = a^1 b^1 (FOR VARIABLES)
           8^5 . 6^6 = 8^5 . 6^6

if you get into a situation like this below this text

           6x^-4vc^5 . -4x^2v^7cd

1. first find the similar variables and group them, this is
   kinda the  opposite of addition of  polynomials which is
   tackled in a previous lecture (ref. L23GPMTH.org)

                 v . v^7 =  v^8
                 x^4 . x^2 = x^6
                 c^5 . c = c^6

   addem da variables and exponents man

2. after that, multiple the  constants and dont do anything
   with the variables

                 6 .  -4 =  -24d (d is  a variable  that so
                                 happens   to  be   in  the
                                 equation)

3. combine them

                 -24dv^8c^6x^6

*** QUOTIENT RULE
If you  are dividing  powers with the  same base,  copy the
base and subtract the exponents 

                  9^6
                  --- = 9^6-4 (9^2)
                  9^4

Always make  sure numerator's  exponent goes first,  if the
numerator is smaller than the denominator's exponent, still
subtract, it will give you a negative output though.

                  a^5
                  --- = a^5-7 (a^-2)
                  a^7

negative exponents will be considered.. for now :))

if there are different bases,  dont even think of trying to
subtract them

                  x^5
                  --- = no. you cant
                  b^4

if you  cant divide the  denominator, you can  do simpliest
form

                  [27]ac^5
                  ------
                  [18]bc^4
*** POWER RULE
if a power is raised to an exponent, multiply the exponents
and dont  consider the factors,  if this section  isnt what
you're looking for,  maybe the "POWER OF  THE PRODUCT RULE"
section might explain when it comes to involving factors) 

        FORMULA: (x^m)^n = x^mn
          (in basic terms, multiply)

        EXAMPLE: (4^3)^2 = 4^ [3 . 2]
                         = 4^6
                         
*** POWER OF THE PRODUCT RULE
The product rule multiplies the factors with the exponents,
to visualize  what this  description meant, please  look at
the example below:

             FORMULA: (xy)^m = x^m . y^m
             
             EXAMPLE: (3b)^2 = 3^2 . b^2
                             = 9b^2
                             (just copy the
                             variables btw) 
                        
*** POWER OF THE QUOTIENT RULE
This rule focuses on  distributing the exponent outside the
exponent  to  the two  bases,  and  we meant  distributing,
copying

             FORMULA: (x/y)^m = x^m/y^m

             EXAMPLE: (4/5)^3 = (4^3/5^3)
                              = 64/125
                              (multiply them with
                              factors) 

*** ZERO RULE
I'll explain  this in  the simpliest way  possible, *ahem*,
anything  with a  zero as  the  exponent is  equal to  one,
anything, well only numbers

               74^0 = 1
               34^0 = 1