c) \( \left(3 \cdot 10^{-3}\right)^{2} \cdot\left(3 \cdot 10^{-2}\right)^{-1} \)

To simplify the expression \( \left(3 \cdot 10^{-3}\right)^{2} \cdot\left(3 \cdot 10^{-2}\right)^{-1} \), we first handle the powers separately. Calculating \( \left(3 \cdot 10^{-3}\right)^{2} \) gives us \( 3^{2} \cdot (10^{-3})^{2} = 9 \cdot 10^{-6} \). Next, for \( \left(3 \cdot 10^{-2}\right)^{-1} \), we find \( \frac{1}{3 \cdot 10^{-2}} = \frac{1}{3} \cdot 10^{2} = \frac{10^{2}}{3} \). Now, we can multiply the two results: \[ \left( 9 \cdot 10^{-6} \right) \cdot \left( \frac{10^{2}}{3} \right) = \frac{9 \cdot 10^{-6} \cdot 10^{2}}{3} = \frac{9 \cdot 10^{-4}}{3} = 3 \cdot 10^{-4}. \] Therefore, the simplified expression is \( 3 \cdot 10^{-4} \).