elementary number theory - Calculate $121^{199} mod 300$

Using Fermat's little theorem I proved that

$$121^{199} = 121^{39} \mod 300$$

(as $\phi(300)$ is $80$) but I don't think I can leave it like this.
My question being how can I solve $121^{39}\hspace{-3mm}\mod 300$. Any ideas, suggestions?