Write 54 as 2·27 and then as 21·33, and
indicate the understood index of the root as 2



Rules for 

1. If M is less than N, then leave it as it is.

2. If M can be divided evenly by N, then it equals 


3. If M is greater than N, then do this division
where Q is the quotient and R is the remainder 

       Q
     N)M
       ...
        R  

Then it equals:







For the 21, since 1 is less than 2, we use rule 1 and do nothing 

For the 33, since the exponent 3 is greater than the index 2,
we use rule 3 and do this division:

       1 
     2)3
       2
       1



For the x7, since 7 is greater than 2, we use rule 3
and do this division:
        
       3 
     2)7
       6
       1

and write:

 and dispose of the 1 exponents:



We can also multiply the 2 by the 3 and dispose of the 2 index and 
we end up with:


     

Edwin