How to solve large exponential using fast exponential modular arithmetic?

Question

How to solve modulus of large exponential like 191^15 mod 719 using fast modular arithmetic with left to right binary form.

Answer 1

Method I
191^15 % 719 
m=191
n=719 
e=15 write in binary 01111
d= binary bits
Three rule to be followed during process 
1.intially d = 1 
2.if d=0 do d^2%n and write it as new d
3.if d=1 do d^2*m % n and write it as new d
 

	0	1	1	1	1
intial d=1 do d^2%n	1	1	531	326	403
m	*	191	191	191	191
d*m%n=new d	1	191	42	432	40

therefore 191^15%719 = 40

Method II(but it wont work for prime power)

191^15 %719 
=(191^3%719)^5
=(42^5%719)
=40