Answer : 4

Solution:

(32^32^32)mod9 = ((-4)^32^32))mod 9

= **(4^32^32)mod 9** (given that minus to even power is positive) ---- (i)

Now

(4^1)mod9 = 4

(4^2)mod9 = 7

(4^3)mod9 = 1

(4^4)mod9 = 4

and so on..

A pattern of 4,7,1 will be repeated

4^(3k+1) will leave remainder 4 when divided by 9

4^(3k+2) will leave remainder 7 when divided by 9

4^(3k) will leave remainder 1 when divided by 9

Now 32 = (3*10 + 2))

Therefore, continuing from (i)

= (4^(3k+2)^32)mod9

= (4^32)mod9

=(4^(3k+2))mod9

=4