If x = 2^8 and x^x = 2^k, what is k?  Choose the correct choice from the following choices.
A) 2^15	B) 2^14	C) 2^13	D) 2^12	E) 2^11
Solution:   We know that x=2^8   which implies x^x = (2^8)^(2^8) = 2^(8 * 2^8) [because (x^y)^z = x^(y*z))]   so 2^(2^3 * 2^8) = 2^(2^(3+8)) [because x^a * x^b = x^(a+b)]   therefore x^x = 2^(2^11)   Given that x^x=2^k   so 2^(2^11) = 2^k   Since the base is same the exponent will also be same   therefore k = 2^11   Answer: 2^11
<result>E</result>
If x = 2^8 and x^x = 2^k, what is k?