Combine exponents with same base: Solve 17^(3.5) × 17^(7.3) ÷ 17^(4.2) = 17^? and find the value of ?.

Introduction / Context:With the same base, multiply by adding exponents and divide by subtracting exponents. This item uses decimal exponents to ensure comfort beyond integers.

Given Data / Assumptions:

• Base 17 throughout
• Expression: 17^(3.5 + 7.3 − 4.2)

Concept / Approach:a^m * a^n = a^(m+n); a^m / a^n = a^(m−n). Apply sequentially: first add 3.5 and 7.3, then subtract 4.2.

Step-by-Step Solution:3.5 + 7.3 = 10.810.8 − 4.2 = 6.6Therefore the expression equals 17^(6.6)

Verification / Alternative check:Rearrange: (3.5 − 4.2) + 7.3 = (−0.7) + 7.3 = 6.6—same result.

Why Other Options Are Wrong:8, 8.4, 6.4, 7.2 stem from arithmetic slips when combining decimals.

Common Pitfalls:Adding all three numbers or misplacing the subtraction; track signs carefully.

Final Answer:6.6