Sixth root interpretation: Evaluate the sixth root of 0.000729.

Introduction / Context: The notation ⁶√(number) means the sixth root. Recognizing perfect powers helps evaluate roots quickly.

Given Data / Assumptions: Compute ⁶√(0.000729).

Concept / Approach: Write 0.000729 as 729 × 10^-6. Since 729 = 3^6, taking the sixth root is straightforward.

Step-by-Step Solution: 0.000729 = 729 × 10^-6.⁶√(729 × 10^-6) = ⁶√(729) × ⁶√(10^-6) = 3 × 10^-1 = 0.3.

Verification / Alternative check: (0.3)^6 = (3 × 10^-1)^6 = 3^6 × 10^-6 = 729 × 10^-6 = 0.000729.

Why Other Options Are Wrong: 0.027, 0.03, 0.09, 0.9 are the square, cube, or other root results but not the sixth root.

Common Pitfalls: Misreading 6√ as 6 × √; here it denotes the sixth root, not 6 times the square root.

Final Answer: 0.3