powers and roots

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by kishore » Sat May 31, 2008 8:01 am
if d=2^64 and d^d=2^p, what is the value of P?

a 64
b 128
c 2^70
d 2^64
e 2^128


Answer is C.

d = 2 ^ 64

d ^ d = (2 ^ 64) ^ (2 ^ 64)
= (2 ^ (2 ^ 6)) ^ (2 ^ 64)
now add the powers (6+64 = 70)

2 ^ p = 2 ^ (2 ^ 70)

=> p = 2 ^ 70