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Question

How many digits are there in 4^4^2+5^5^2


Solution

4^4^2=4^(4*4)
     =4^16
     =4*4*4*4*4*4*4*4*4*4*4*4*4*4*4*4.  (16 times)
=(4*4*4*4)*(4*4*4*4)*(4*4*4*4)*(4*4*4*4)
=256*256*256*256
=(256*256)*(256*256)
=65536*65536
=4294967296
Now
5^5^2=5^(5*5)
=5^25
=(5*5*5*5*5)*(5*5*5*5*5)*(5*5*5*5*5)*(5*5*5*5*5)*(5*5*5*5*5)
=3125*3125*3125*3125
*3125
=9765625*9765625*3125
=95367431640625*3125
=298023223876953125
Now
4^4^2+5^5^2
=4294967296+298023223876953125
=298023228171920421
There are 18 digits in 4^4^2+5^5^2

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