If x = 3^27 and x^x = 3^k, what is k?	Options.
A) 3^9	B) 3^12	C) 3^27	D) 3^30	E) 3^33
Solution:   We know that x=3^27   which implies x^x = (3^27)^(3^27) = 3^(27 * 3^27) [because (x^y)^z = x^(y*z))]   so 3^(3^3 * 3^27) = 3^(3^(3+27)) [because x^a * x^b = x^(a+b)]   therefore x^x = 3^(3^30)   Given that x^x=3^k   so 3^(3^30) = 3^k   Since the base is same the exponent will also be same   therefore k = 3^30   Answer: 3^30
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If x = 3^27 and x^x = 3^k, what is k?