Combine exponents by converting all factors to base 7: Evaluate the exponent ? in 7^8.9 ÷ (343)^1.7 × (49)^4.8 = 7^?.

Introduction / Context:
When multiple terms share a common prime base after conversion, you can add and subtract exponents to combine them. Here, 343 and 49 convert to powers of 7, letting us compute a single resultant exponent exactly.

Given Data / Assumptions:

• 343 = 7^3 and 49 = 7^2.
• Expression: 7^8.9 ÷ (7^3)^1.7 × (7^2)^4.8.

Concept / Approach:
Use (a^m)^n = a^(mn) and the rules: division subtracts exponents, multiplication adds exponents. Keep decimals as exact tenths to avoid rounding slips.

Step-by-Step Solution:

Verification / Alternative check:
Group as 7^(8.9 + 9.6) / 7^5.1 = 7^(18.5) / 7^5.1 = 7^(13.4). Consistent.

Why Other Options Are Wrong:

• 12.8, 11.4, 9.6: Each misses one conversion or uses the wrong sign when dividing.

Common Pitfalls:
Forgetting to multiply exponents when raising a power to a power, and sign errors when dividing.

Final Answer: