Power and base pattern recognition: Evaluate (0.49)^4 × (0.343)^4 ÷ (0.2401)^4 and express it as (70/100)^?. Determine the integer exponent ?.

Introduction / Context:
This problem checks your ability to convert recurring decimal bases into powers of a common prime (here, 7) over powers of 10 and then simplify using exponent rules. The goal is to match the simplified result to a clean form (70/100)^?.

Given Data / Assumptions:

• Compute (0.49)^4 × (0.343)^4 ÷ (0.2401)^4.
• Express the final answer as (70/100)^?.
• All exponents are integers and operations follow standard power rules.

Concept / Approach:
Rewrite each decimal with base 7 and 10: 0.49 = 7^2/10^2, 0.343 = 7^3/10^3, 0.2401 = 7^4/10^4. Apply exponent laws to combine the powers, then simplify the net exponents to match the target base 70/100 = 7/10.

Step-by-Step Solution:

Verification / Alternative check:
Numerically, 0.7^4 = 0.2401, which is consistent with the original decimal pattern.

Why Other Options Are Wrong:
3, 1, 2, and 7 do not match the simplified exponent balance. Only 4 preserves the equality.

Common Pitfalls:
Mixing addition and subtraction of exponents, or failing to recognize that dividing by (7^4/10^4)^4 subtracts powers in both numerator and denominator.

Final Answer:
4