First of all its
given 25^25^25 and not ((25)^25)^25. Difference is that
the topmost 25 in the exponent term is for the other 25 in the exponent only
and not for the base 25.
Then we first divide
the base 25 by 9 which gives remainder 7. Now we consider the exponent term, i.e.,
25^25 and divide it with 6, i.e, the phi (N) (read as phi of N) value for 9.
phi (N)= Nos.less
than or equal to N and prime to it.
To calculate phi (N)
we us the following Euler's formula:
If N= a^x*b^y*c^z.... then phi (N)= N(11/x)(11/y)(11/z).........
where a,b,c.... are the prime factors for N.
Note: To use the
above method we need to ensure that N (in this case 9) is coprime with p (in
this case 25).
Thus, on dividing the
exponent 25^25 by 6, we get 1^25=1.
Thus now we are left
with 7^1/9 which is 7 only.
So Answer is 7.
