if x = 3 ^ 9 and x ^ x = 3 ^ k , what is k ?
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 answer : a
multiply(power(3, 9), 9)