Alright so we are playing Senior Eq and I call base 12 and k11, and set the goal (6^93)/root. What if I told you that you could solve this in about 30 seconds?
To figure out the cycle length what you have to do is take the effective K, which is 121 in this instances, and prime factorize it, so you get 11^2. To find the cycle length, you take the the lcm of the factors minus one and the power with the exponent reduced by one, so in this case (11-1) and (11^1), which is 110. Making sure the k and base are relatively prime, you know your cycle length is 110. Since the goal adjusted for base is 6^111 / 11, your answer should equal 6/11.
Example problem: 5^88/7 K7