Evaluating $48^{322} \pmod{25}$ How do I find $48^{322} \pmod{25}$?

Finding the $\phi(n)$ for $25$ was easy, but what it if the $n$ was arbitrarily large?
$$48 \equiv -2( \mod 25)$$
Playing around with $-2(\mod 25)$ so as to get $1$ or $-1(\mod 25)$.
We see that $1024 \equiv -1(\mod 25)$
$$((-2)^{10})^{32} \equiv 1 (\mod 25)$$
$$(-2)^{322} \equiv  4(\mod 25)$$
