For an elliptic curve defined over a field $K$, how to perform operations to calculate the coordinates if the points lies in another field $K'$?

Question

Let $E$ be an elliptic curve defined by the equation $E:y^2=x^3+ax+b$ over the field $K$ i.e. $a$, $b$ are elements of $K$. Let’s have another field $K’$ and let’s take a couple $(x,y)$ element of $E(K′)$, how to calculate say “$ax$” while $a$ is an element of $K$ and $x$ is an element of another field $K′$. I know it's possible if $K'$ is a field extension of $K$. But how to perform the operation? Is $a$ taken as an element of $K'$ or as a coefficient in $K$?