Code:

Mod(10,107)^100000000000000000000000000000000000000000
Mod(34, 107)
##
*** last result computed in 0 ms

.

It actually works by

left-right binary exponentiation modulo n
And since 107 is prime we can use

Fermat's little theorem:

Code:

Mod(10,107)^(100000000000000000000000000000000000000000%106)
Mod(34, 107)

Or simething even "bigger":

Code:

Mod(10,107)^(100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000%106)
Mod(4, 107)