1. The problem is to simplify the expression $\left(0.1 \times 10^{-3}\right)^{-2}$.\n\n2. Recall the rule for powers of a product: $\left(ab\right)^n = a^n b^n$. Also, the rule for negative exponents: $x^{-n} = \frac{1}{x^n}$.\n\n3. Apply the power to each factor inside the parentheses:\n$$\left(0.1 \times 10^{-3}\right)^{-2} = 0.1^{-2} \times \left(10^{-3}\right)^{-2}$$\n\n4. Simplify each term:\n- $0.1 = 10^{-1}$, so $0.1^{-2} = \left(10^{-1}\right)^{-2} = 10^{2}$\n- $\left(10^{-3}\right)^{-2} = 10^{6}$\n\n5. Multiply the results:\n$$10^{2} \times 10^{6} = 10^{2+6} = 10^{8}$$\n\n6. Therefore, the simplified expression is:\n$$\boxed{10^{8}}$$\n\n7. Among the options given, $100 \times 10^{6}$ equals $10^{2} \times 10^{6} = 10^{8}$, which matches our result.