$K$ is a field and $R = K[X] / (X^n)$ with $n \in \mathbb{Z}_{\geq 1}.$ Furthermore, $x$ is denoted by $x:= X+ (X^n) \in R$ and the equivalence class $r$ in $R$ is represented by $r=a_0 + a_1 X + \cdots+ a_{n-1} X^{n-1},$ with $a_i \in K.$
I have asked a question about this field earlier asking for help showing that $r$ is a unit iff $a_0 \neq 0$ and has an inverse, the answer to which greatly helped me. I have since proven that every zero divisor in $R$ is nilpotent.
I am now trying to find a ring isomorphism $K [X] / ((X-a)^n) \cong K [X] / (X^n)$ for every $a \in K,$ but am not sure how to proceed.
Any help would be appreciated.