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

Question

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Let's simplify the expression step by step:

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

1. **Square the first term:**
   
   $$
   \left(3 \cdot 10^{-3}\right)^{2} = 3^{2} \cdot \left(10^{-3}\right)^{2} = 9 \cdot 10^{-6}
   $$

2. **Take the reciprocal of the second term:**
   
   $$
   \left(3 \cdot 10^{-2}\right)^{-1} = \frac{1}{3} \cdot 10^{2}
   $$

3. **Multiply the results from steps 1 and 2:**
   
   $$
   9 \cdot 10^{-6} \cdot \frac{1}{3} \cdot 10^{2} = \left(9 \cdot \frac{1}{3}\right) \cdot \left(10^{-6} \cdot 10^{2}\right) = 3 \cdot 10^{-4}
   $$

**Final Answer:**
$$
3 \cdot 10^{-4}
$$
The simplified result is $$ 3 \times 10^{-4} $$.

c)

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