Rational Exponents and Simplification

The video tutorial explains how to simplify expressions using rational exponents. It begins with an introduction to the concept of rational exponents and their relation to radicals. The tutorial then provides three examples: simplifying the square root of 25, the cube root of 64x^3, and the fourth root of 81x^1y^8z^12. Each example demonstrates the process of converting the radical expression into a rational exponent form and simplifying it by applying exponent rules.

What does the denominator of a rational exponent indicate?

• The base of the exponent

• The index of the radical

• The coefficient of the base

• The power of the base

How is the square root of a number expressed using rational exponents?

• x^(2/3)

• x^2

• x^(1/2)

• x^(1/3)

What is the simplified form of 25^(1/2)?

• 10

• 15

• 20

• 5

What is the cube root of 64x^3 expressed as a rational exponent?

• (64x^3)^(1/2)

• (64x^3)^(1/3)

• (64x^3)^(3/2)

• (64x^3)^(2/3)

What is the prime factorization of 64?

• 2^5

• 3^4

• 2^6

• 4^3

What is the simplified form of (64x^3)^(1/3)?

• 16x

• 2x

• 4x

• 8x

How is the fourth root of a number expressed using rational exponents?

• x^(1/5)

• x^(1/2)

• x^(1/3)

• x^(1/4)

What is the simplified form of 81^(1/4)?

• 9

• 12

• 6

• 3

What is the simplified form of y^8 raised to the power of 1/4?

• y^3

• y^1

• y^4

• y^2

What is the final simplified form of the expression (81x^1y^8z^12)^(1/4)?

• 3x^(1/3)y^2z^4

• 3x^(1/4)y^2z^3

• 3x^(1/4)y^3z^2

• 3x^(1/2)y^3z^2