### Simplification Methods Survey

I noted that SageMath has many ways to simplify expressions, including simplify_full(), full_simplify and canonicalize_radical.
Is there a survey nd usage guide available for these?
In particular, I am trying to simplify an expression as in

`constants=var('a1,a2,b,c')

((a1*b)^c/(a2*b)^c).simplify_full()`

such that I get `(a1/a2)^c`

, but without success.