137^(13^47)

Hi Akshay, what is the question?

unit digit pucha h kya wo to bata skte h.

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

So the units digit of (137^13)^47 is 3.