To solve the equation \( x^3 = 64 \), we need to find the value of \( x \) such that its cube equals 64.

### Step-by-step solution:
1. Start with the equation:
   \[
   x^3 = 64
   \]
2. To solve for \( x \), take the cube root of both sides:
   \[
   x = \sqrt[3]{64}
   \]
3. Since \( 64 = 4^3 \), the cube root of 64 is:
   \[
   x = 4
   \]

Thus, \( x = 4 \) is the solution.

Would you like a more detailed explanation or have any questions?

Here are some related questions to consider:
1. How do you calculate cube roots for negative numbers?
2. What is the general method for solving equations involving higher powers, like \( x^n \)?
3. How do cube roots apply in real-world scenarios?
4. Can equations like \( x^3 = 64 \) have multiple solutions in complex numbers?
5. How does cube root differ from square root in terms of their geometric interpretations?

**Tip:** To check your solution, always substitute the value of \( x \) back into the original equation to verify it works.

Learn how to solve the cubic equation x^3 = 64 with a detailed, step-by-step solution. Understand cube roots and how to calculate them. This problem covers key algebraic concepts such as exponents and cube roots, and is suitable for students in Grades 8-10.

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