The following may be off-topic, but I'd like to share an alternate simplification.
There are many ways to "simplify" algebraic expressions. Expressions in beginning courses are often cooked up for practicing specific definitions, properties and/or rules.
Later on, when we use our skills to algebraically manipulate given information, there might be a specific goal in mind concerning a specific application in the real world.
For example, later on we might be working with exponential growth over time (of some chemical reaction, perhaps), using a model like this:
y = a*b^t
Let's say the expression given in this thread is an example of some potential data from chemistry experiments. We may simplify it to obtain the exponential form above (treating n as the time variable).
y = (9/125)*(3/125)^n
a = 9/125
b = 3/125
t = n
This alternate simplification can be obtained by applying definitions and proprties, just like the OP did, but with a different goal in mind.