Describe the elemets of $I^n$

Describe the elemets of $I^n$

I had a question in which encounters to ideal multiplication. My approach
to this problem force me to find out the $I^n$ structure as described
below:
suppose $R$ is a ring and $I\unlhd R$. identify the $I^n$ set
($n\in\mathbb{N\cup\{0\}}$) by describing it's elements when:
1- $I$ is finitely generated.
2- $I$ is an arbitrary ideal in $R$.
to prove, take $R$ commutative, with identity or without these presumes.
I doubt if there is a clear answer to part 2 above. would you solve this
problem?
Thanks in advance.