But how many 4^4 are there in the left side of the equality: 4^4 * 4^4 *....4^4 = 4^(4^4)

Question

There are 2 books sitting side by side, consisting of exactly 100 pages.
The book on the left is upside down.
If you add the page number at the extreme left side of the book on the left to the page number at the extreme right side of the right hand side book, what is the total?

Answer 1

If N = number of 4^4 on the left side
4^(4+4+4+4+4...........) = 4^(4^4)
4^(N*4) = 4^(4^4)
N*4 = 4^4 { Equating the powers on LHS and RHS }
N = 4^4/4 = 4^3 = 64
which means there are 64 terms (4^4) in the LHS.

Answer 2

64
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