solution: Rewriting $\frac{4321}{5^7\cdot2^8}$ as a decimal with a denominator of $5^8\cdot2^8=10^8$, we have \[ \frac{4321}{5^7\cdot2^8}\cdot\frac{5^{1}}{5^{1}}=\frac{4321\cdot5}{10^8}=\frac{21605}{10^{8}}=0.00021605.\]So, the sum of the digits of the decimal representation is $2+1+6+0+5 = \boxed{14}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  What is the sum of the digits in the terminating decimal representation of the fraction $\frac{4321}{5^7\cdot2^8}$?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 14
extra_info.question: What is the sum of the digits in the terminating decimal representation of the fraction $\frac{4321}{5^7\cdot2^8}$?
extra_info.split: test