Simplifying the cube root of an expression with variables

The video tutorial explains how to simplify a radical expression involving the cube root of 27 times X to the 9th. It emphasizes the importance of understanding perfect cube numbers and demonstrates two methods for simplification: using prime factorization and grouping terms. The tutorial provides a step-by-step approach to simplify the expression, resulting in 15 times X cubed.

What is the cube of 3?

• 6

• 81

• 9

• 27

Which of the following is a perfect cube?

• 27

• 45

• 16

• 64

What is the prime factorization of 27?

• 3 * 3 * 3

• 2 * 2 * 2

• 5 * 5 * 5

• 7 * 7 * 7

How many groups of three X's are there in X to the 9th power?

• 4

• 1

• 3

• 2

What is the simplified form of 5 times the cube root of 27 * X to the 9th?

• 27X

• 5X

• 15X^3

• 3X^3