To convert \(3.875 \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10}\) meters to kilometers, we first simplify the expression.
We have:
\[ 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} \times 10^{10} = 10^{90} \]
So,
\[ 3.875 \times 10^{90} \text{ meters} \]
Next, to convert meters to kilometers, we know that:
\[ 1 \text{ kilometer} = 1,000 \text{ meters} = 10^3 \text{ meters} \]
Thus, to convert meters to kilometers, we divide by \(10^3\):
\[ \frac{3.875 \times 10^{90}}{10^3} = 3.875 \times 10^{90 - 3} = 3.875 \times 10^{87} \text{ kilometers} \]
Therefore, the final answer is:
\[ \boxed{3.875 \times 10^{87}} \text{ km} \]