Answer
$\frac{1}{10^4}.$
Work Step by Step
We simplify by using the rules of the exponents as follows:
$$
\frac{10^8 \cdot 10^{-6}}{(10^{-3})^{-2}}=\frac{10^{8-6}}{10^{-3*-2}}=\frac{10^2}{10^6}=\frac{1}{10^4}.
$$
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