Cube Roots and Exponent Rules

The video tutorial explains how to simplify cube roots by identifying perfect cube factors through prime factorization. It covers examples such as the cube root of 64, negative 125, 27x^6, and x^9y^3z^12, demonstrating the process of breaking down numbers and variables into their prime factors and grouping them into perfect cubes. The tutorial emphasizes the use of exponent rules and provides alternative methods for simplification.

What is the first step in simplifying cube roots?

• Dividing the radicand by 3

• Finding the square root of the radicand

• Identifying perfect cube factors

• Multiplying the radicand by 2

What is the cube root of 64?

• 2

• 5

• 3

• 4

How can negative 125 be expressed to show it is a perfect cube?

• -10 times -10 times -10

• -5 times -5 times -5

• 10 times 10 times 10

• 5 times 5 times 5

What is the cube root of negative 125?

• -25

• 25

• 5

• -5

What is the cube root of 27x^6?

• 9x

• 3x

• 9x^2

• 3x^2

How can x^6 be expressed to identify perfect cube factors?

• x^4 times x^2

• x times x times x

• x^2 times x^2 times x^2

• x^3 times x^3

What is the cube root of x^9?

• x^4

• x^3

• x^2

• x^5

What is the cube root of y^3?

• y^4

• y

• y^3

• y^2

What is the cube root of z^12?

• z^4

• z^3

• z^5

• z^2

Which exponent rule is used when multiplying bases with the same exponent?

• a^m - a^n = a^(m-n)

• a^m + a^n = a^(m+n)

• a^m * a^n = a^(m+n)

• a^m / a^n = a^(m-n)