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 $2+1+6+0+5 = \boxed{14}$.
Question:
What is the sum of the digits in the terminating decimal representation of the fraction $\frac{4321}{5^7\cdot2^8}$?
Answer:
Let's think step by step.

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14
What is the sum of the digits in the terminating decimal representation of the fraction $\frac{4321}{5^7\cdot2^8}$?
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