If x = 3^9 and x^x = 3^k, what is k?	Choose the correct choice from the following choices:
A) 3^11
B) 3^13
C) 3^25
D) 3^27
E) 3^81
Solution:   We know that x=3^9   which implies x^x = (3^9)^(3^9) = 3^(9 * 3^9) [because (x^y)^z = x^(y*z))]   so 3^(3^2 * 3^9) = 3^(3^(2+9)) [because x^a * x^b = x^(a+b)]   therefore x^x = 3^(3^11)   Given that x^x=3^k   so 3^(3^11) = 3^k   Since the base is same the exponent will also be same   therefore k = 3^11   3^11nswer: 3^11
<result>A</result>
If x = 3^9 and x^x = 3^k, what is k?