So here is the mod function:
$$5 ^ {31} \cdot 2 ^{789} - 23^{23}\pmod{10}$$
Is there a way to shorten it, or I must calculate it plain numbers? I have tried the mod powers rule, but except for the $23$ the others remain unchanged. It is strange because none of the known (to myself) mod rules fit.
Since $3^2\equiv -1\pmod {10}$, one has
$$\begin{align}5^{31}\cdot 2^{789}-23^{23}&\equiv0-3^{23}\\&\equiv -(3^2)^{11}\cdot 3\\&\equiv -(-1)^{11}\cdot 3\\&\equiv -(-1)\cdot 3\\&\equiv 3.\end{align}$$