If x = 6^36 and x^x = 6^k, what is k?	Choose the correct choice from the following
A) 6^36	B) 6^38	C) 6^72	D) 6^216	E) 6^432
Solution:   We know that x=6^36   which implies x^x = (6^36)^(6^36) = 6^(36 * 6^36) [because (x^y)^z = x^(y*z))]   so 6^(6^2 * 6^36) = 6^(6^(2+36)) [because x^a * x^b = x^(a+b)]   therefore x^x = 6^(6^38)   Given that x^x=6^k   so 6^(6^38) = 6^k   Since the base is same the exponent will also be same   therefore k = 6^38   Answer:6^38
<result>B</result>
If x = 6^36 and x^x = 6^k, what is k?