Prime Factorization and Cube Roots

The video tutorial explains how to simplify cube roots by finding perfect cube factors. It starts with simplifying the cube root of 128x by determining its prime factorization and identifying perfect cubes. The expression simplifies to 4 times the cube root of 2x. Next, the tutorial addresses the cube root of 243x^11, again using prime factorization to find perfect cubes. The expression simplifies to -6x^3 times the cube root of 9x^2. The tutorial emphasizes understanding prime factorization and recognizing perfect cubes to simplify expressions effectively.

What is the first step in simplifying a cube root?

• Multiplying by three

• Dividing by two

• Finding the square root

• Identifying perfect cube factors

What is the prime factorization of 128?

• 3^5

• 5^3

• 2^7

• 2^6

How many factors of two are there in the prime factorization of 128?

• Eight

• Seven

• Six

• Five

What is the simplified expression for the cube root of 128x?

• 16 times the cube root of 2x

• 4 times the cube root of 2x

• 2 times the cube root of x

• 8 times the cube root of x

What is the prime factorization of 243?

• 3^4

• 5^3

• 3^5

• 2^5

How many factors of three are there in the prime factorization of 243?

• Four

• Five

• Six

• Seven

What is the simplified expression for the cube root of 243x^11?

• Negative six x cubed times the cube root of nine x squared

• Negative two x cubed times the cube root of nine x squared

• Negative six x squared times the cube root of nine x squared

• Negative two x squared times the cube root of nine x squared

How many x^3 are there in x^11?

• Five

• Four

• Three

• Two

What is the cube root of x^3?

• x^4

• x^3

• x^2

• x

What is the result of multiplying negative two by three and x cubed?

• Negative two x squared

• Negative two x cubed

• Negative six x squared

• Negative six x cubed