solution: Following exponent laws, ${(3^k)}^6=3^{6k}$.  Because $3^{6k}=3^6$, we have $6k=6$, which, dividing by 6, solves to $k=\boxed{1}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Find $k$, if ${(3^k)}^6=3^6$.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 1
extra_info.question: Find $k$, if ${(3^k)}^6=3^6$.
extra_info.split: test