Question

find the remainder when 27^40 is divided by 12

Answer 1

27^40=3^120
3^3= 3 (mod 12)  (3 is the remainder when 3^3 is divided by 12)
3^3^40=3^40 (mod 12)
again,
3^3=3 (mod 12)
3^3^13 x 3=3^13 x 3 (mod 12)
thus,
3^14=3^6(mod 12)
3^6=3^2 (mod 12)
now since 3^2=9 is less than 12 therefore the remainder is 9. 

Answer 2

Answer:

Step-by-step explanation:

Step 1 27^40 break it down into (3^3)^40 therefore 3^120

Step 2 using (x^n - a^n) is divisible by (x - a) for all the values of n

           x= 3,  n=120 and we will assume a=9

Step 3  (3^120 - 9^120) is divisible by (3-9)

            3-9=6 so    

Step 4 according to the formula 9 is the remainder when 27^40 is divided by 12