Express decimal powers with a common base: Evaluate (0.49)^4 * (0.343)^4 ÷ (0.2401)^4 and write the result as (70/100)^k. Find k.

Introduction / Context:
Recognizing prime-power structure in decimals allows fast simplification. Here, 0.49, 0.343, and 0.2401 are powers of 7 divided by matching powers of 10. The expression reduces neatly to a single power of 7/10.

Given Data / Assumptions:

• Compute E = (0.49)^4 * (0.343)^4 ÷ (0.2401)^4.
• Express E as (70/100)^k = (7/10)^k and determine k.

Concept / Approach:
Rewrite each decimal: 0.49 = 7^2/10^2, 0.343 = 7^3/10^3, 0.2401 = 7^4/10^4. Apply exponent rules to combine and subtract powers when dividing.

Step-by-Step Solution:

Verification / Alternative check:
Since 0.7^4 = 0.2401, the conclusion that E = (0.7)^4 is consistent with the given numbers.

Why Other Options Are Wrong:
1, 2, 3, and 7 do not match the net exponent after combining powers; only 4 preserves the equality.

Common Pitfalls:
Adding instead of subtracting exponents during division, or misidentifying the decimal-to-fraction conversions.

Final Answer:
4