I have this equation (identity?):

$$3^{3x}=3^{2y+1}$$

I understand that this simplifies to:

$$3x=2y+1$$

So, the base (of the exponentials) cancel out. I want to know, what the process/function of this cancelling out is?

I know that you can cancel out exponents by $n$th-rooting the exponents. So by what function do you cancel out the base? 

Please tell me if I should give more information. This is probably a very basic step in dealing with algebraic formulas, but I can't find the specific steps anywhere. I want to know the function so I know what steps to use and how/why they work.

Thanks in advance!