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.