1. **State the problem:** Simplify the expression $$\frac{4 \times 10^{6}}{2 \times 10^{3}}$$. 2. **Recall the rule for division of powers with the same base:** $$\frac{a \times 10^{m}}{b \times 10^{n}} = \frac{a}{b} \times 10^{m-n}$$ where $a$ and $b$ are numbers, and $m$, $n$ are exponents. 3. **Apply the rule:** $$\frac{4 \times 10^{6}}{2 \times 10^{3}} = \frac{4}{2} \times 10^{6-3}$$ 4. **Simplify the fraction:** $$\frac{\cancel{4}}{\cancel{2}} = 2$$ 5. **Calculate the exponent difference:** $$10^{6-3} = 10^{3}$$ 6. **Combine the results:** $$2 \times 10^{3}$$ 7. **Final answer:** $$2 \times 10^{3}$$ which equals 2000.