1. **State the problem:** Divide the numbers written in scientific notation: $$\frac{4.6 \times 10^{4}}{2.5 \times 10^{-5}}$$. 2. **Recall the division rule for scientific notation:** When dividing numbers in scientific notation, divide the coefficients and subtract the exponents of 10: $$\frac{a \times 10^{m}}{b \times 10^{n}} = \frac{a}{b} \times 10^{m-n}$$. 3. **Apply the rule:** $$\frac{4.6}{2.5} \times 10^{4 - (-5)} = 1.84 \times 10^{9}$$. 4. **Explain the steps:** - Divided 4.6 by 2.5 to get 1.84. - Subtracted the exponents: $4 - (-5) = 4 + 5 = 9$. - Combined the results to get the final answer in scientific notation. **Final answer:** $$1.84 \times 10^{9}$$.