1. **State the problem:** Calculate the value of $$C = \frac{4 \times 10^{-7} \times 45 \times (10^3)^2}{12 \times 10^{-3}}$$. 2. **Recall the rules:** When working with powers of 10, use the property $$a^m \times a^n = a^{m+n}$$ and for division $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the numerator:** $$4 \times 10^{-7} \times 45 \times (10^3)^2 = 4 \times 45 \times 10^{-7} \times 10^{6} = 180 \times 10^{-1}$$ 4. **Simplify the denominator:** $$12 \times 10^{-3}$$ 5. **Rewrite the expression:** $$C = \frac{180 \times 10^{-1}}{12 \times 10^{-3}}$$ 6. **Divide the coefficients:** $$\frac{180}{12} = 15$$ 7. **Divide the powers of 10:** $$\frac{10^{-1}}{10^{-3}} = 10^{-1 - (-3)} = 10^{2}$$ 8. **Combine results:** $$C = 15 \times 10^{2} = 15 \times 100 = 1500$$ **Final answer:** $$C = 1500$$