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 cube root of a number asking for?

• A number multiplied by itself four times

• A number multiplied by itself once

• A number multiplied by itself twice

• A number multiplied by itself three times

Which of the following is the correct prime factorization of 64?

• 8 * 8

• 4 * 4 * 4

• 2 * 2 * 2 * 2 * 2 * 2

• 2 * 2 * 2 * 2 * 2

How many times is the number 2 multiplied by itself in the prime factorization of 64?

• Three times

• Four times

• Six times

• Two times

What is the cube root of X^3?

• X

• X^2

• X^3

• 1

What is the final answer when taking the cube root of 64X^3?

• 16X

• 2X

• 4X

• 8X