Remainder with congruences I'm having some trouble understading how to use congruence to solve this type of exercises:

a) Determinate the remainder of the division of $2173451$ with $17$
b) Determinate the remainder of the division of $1522^{1000}$ with $19$

For example, in b) I know that $1522=80\times19+2$, so $1522 \equiv 2(mod19)$ , so  $1522^{1000} \equiv 2^{1000}(mod19)$. What now?
In exercise $b)$ , reduce the exponent modulo $\phi(19)=18$
note that $$127850\cdot 17=2173450$$ and $$1522^9 \equiv -1 \mod 19$$