How to calculate mapping in bilinear I am trying to read a paper in cryptography. In key generation phase, paper give a definition for bilinear like G and Gt be two cyclic groups of prime order p

$e: G * G \to G_t$.  be a map with the following properties:


and in one place i found a definition like


my doubt is in the last part. Specifically in m.e(g1,gn)^t
suppose m is any message, g1=3,gn=13 t=6 (for more information v=5,gi=10.no problem whether all the value assumptions are true or not). then how can i compute e(g1,gn)^t part? sorry for my bad math notation
According to PBC manual, Pairing functions, map $\hat e(,)$ (without t-power) could be calculated as follows:

pairing_pp_t pp;
pairing_pp_init(pp, g1, pairing);
pairing_pp_apply(r1, gn, pp); // r1 = e(g1, gn)
pairing_pp_clear(pp);


Before calculating the map, pairing parameters must be initialized.