If x^3 = 6^2 - 3^2, what is the exact value of x?

Introduction / Context:
This question tests basic exponent evaluation and cube roots. The right-hand side is a simple difference of squares, and once it is computed, the equation becomes x^3 = 27, whose cube root is a standard value. The key is to compute 6^2 and 3^2 correctly and not confuse x^3 with 3x.

Given Data / Assumptions:

• x^3 = 6^2 - 3^2
• Compute squares first, then take cube root.

Concept / Approach:
Evaluate powers: 6^2 and 3^2. Subtract to get a number. Then solve x^3 = that number by taking the cube root (the number whose cube equals the given value).

Step-by-Step Solution:

Verification / Alternative check:
Plug back: If x = 3, then x^3 = 27. RHS is 36 - 9 = 27. Both sides match exactly, so x = 3 is correct.

Why Other Options Are Wrong:

Common Pitfalls:
Misreading x^3 as 3x, computing 6^2 - 3^2 as 3^2 (wrong), or forgetting cube root vs square root.

Final Answer:
3