induction n; intuition; simpl in *.
symmetry.
eapply ratMult_1_l.
rewrite IHn.
repeat rewrite <- ratMult_assoc.
eapply ratMult_eqRat_compat; intuition.
repeat rewrite ratMult_assoc.
eapply ratMult_eqRat_compat; intuition.
eapply ratMult_comm.
Qed.

Lemma expRat_exp_prod : forall n1 n2 r,
expRat r (n1 * n2)%nat == expRat (expRat r n1) n2.