If x = 4^16 and x^x = 4^k, what is k?  Select the correct option: A) 4^14 B) 4^16 C) 4^18 D) 4^20 E) 4^22
Solution:   We know that x=4^16   which implies x^x = (4^16)^(4^16) = 4^(16 * 4^16) [because (x^y)^z = x^(y*z))]   so 4^(4^2 * 4^16) = 4^(4^(2+16)) [because x^a * x^b = x^(a+b)]   therefore x^x = 4^(4^18)   Given that x^x=4^k   so 4^(4^18) = 4^k   Since the base is same the exponent will also be same   therefore k = 4^18   Answer:4^18
<result>C</result>
If x = 4^16 and x^x = 4^k, what is k?