Simplifying the cube root of an expression using prime factorization

The video tutorial explains how to find the cube root of 64X^3. It begins with an introduction to cube roots and the problem setup. The teacher demonstrates using prime factorization to break down the number 64 into its prime factors. The solution involves identifying the number that, when multiplied by itself three times, equals 64, which is 2. The teacher then applies the same logic to find the cube root of X^3, which is X. The final answer is calculated as 4X, combining the results of both parts of the problem.

What is the significance of the expression X^3 when taking the cube root?

What is the final answer when calculating the cube root of 64X^3, and how is it derived?