Question: User: 6.1 \times 10^{8} \times 8.5 \times 10^{2} = ______ \times 10____ [2] solve
1. **State the problem:** We need to multiply $6.1 \times 10^{8}$ by $8.5 \times 10^{2}$ and express the result in the form $a \times 10^{b}$.
2. **Recall the multiplication rule for powers of 10:** When multiplying numbers in scientific notation, multiply the decimal parts and add the exponents of 10.
3. **Multiply the decimal parts:**
$$6.1 \times 8.5 = 51.85$$
4. **Add the exponents:**
$$8 + 2 = 10$$
5. **Combine the results:**
$$51.85 \times 10^{10}$$
6. **Adjust to proper scientific notation:** The decimal part must be between 1 and 10, so rewrite $51.85$ as $5.185 \times 10^{1}$.
7. **Apply this adjustment:**
$$5.185 \times 10^{1} \times 10^{10} = 5.185 \times 10^{1+10} = 5.185 \times 10^{11}$$
**Final answer:**
$$5.185 \times 10^{11}$$