Exponent Laws

As you all know, we went back in time a few days ago, back... to grade 9. For those of you who weren't there, here is the review on Exponent Laws (Power Laws) .

Rule #1 When multiplying with exponents, simply add the exponents and the equation will become much simpler.

for example:
                     3         8    <--- they're exponents okay?
                ( x     ) ( x    )
                     
               Since both constants in the equation are the same, you can add the exponents.

                    3    +  5          8
                ( x   ) ( x   ) = ( x   )

Of course, you could always write out the equation like this:

                    3       5                                                8
                ( x   ) ( x   ) = (x*x*x) + (x*x*x*x*x) = x

But. People who do math professionally (or anyone who has done it frequently) will know that we are incredibly lazy when it comes to work and always take the shortest route to whatever we are trying to do, so use the first equation (this also applies to all exponent laws that will appear on this post).


Rule #2

When dividing with exponents that have the same constant, simply subtract the exponents from each other.

ex.       5     3        2                                                                                                        
         x    / x    =  x                                                                                                                          
                                                                                                                                                           

Rule #3   

If a constant ever has an exponent of  "0", then the product will always be one.

ex.         0
           x    = 1


Rule #4
                                                                                        5   3    
When a power is the base of another power, like this:  ( x      )     multiply the two exponents together to get one exponent in order to simplify the equation. so it'll look like this:          15
                                                                                                        ( x      )                              

Rule #5

When dividing an exponent by an exponent with an exponent base outside the exponent equation  
                       m   t
 like this:    (  x  )          
                 ____           multiply the inner exponents by the outer exponent (multiply m + n by t).
                       n                
                 ( y     )

Rule #6

If you have a power with a negative exponent it can be written as the reciprocal with a positive exponent.
                            -3          
In other words:   3      =    _1_
                                          3

If I have left anything out from the lesson plans, feel free to comment, or tell me in class when you see me.