Question

Find the unit place digit of ((137)^13)^47​

Answer 1

Step-by-step explanation:

((137)^13)^47

137^611

The unit place is 3

Answer 2

Power of 7 have units digit cycling through 7,9,3,1.

i.e.

7^1 => 7

7^2 => _9

7^3 => __3

7^4 => ___1

7^5 => ___7

and so on

137^13 = 137^12 * 137^1 = (137^4)^3 * 137^1 = 1^3 * 7 = 7

Again 7^47 = 7^44 * 7^3 = (7^4)^11 * 7^3 = 1 * 3