6-2 Rational Exponents Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

Warm Up Simplify each expression. 1. 2. 3. 4.

Essential Question How do you you evaluate and simplify expressions containing rational exponents?

Recall that the radical symbol is used to indicate roots. The index is the small number to the left of the radical symbol that tells which root to take. For example represents a cubic root. Since 23 = 222 = 8 .

Another way to write nth roots is by using fractional exponents Another way to write nth roots is by using fractional exponents. For example, for b >1, suppose Square both sides. Power of a Power Property b1 = b2k 1 = 2k If bm = bn, then m = n. Divide both sides by 2. So for all b > 1,

When b = 0, When b = 1, Helpful Hint

Additional Example 1: Simplifying b Simplify each expression. A. b 1 n Use the definition of . = 7 B. b 1 n Use the definition of . = 2 + 3 = 5

Simplify each expression. Check It Out! Example 1 Simplify each expression. a. b 1 n Use the definition of . = 3 b. b 1 n Use the definition of . = 11 + 4 = 15

A fractional exponent can have a numerator other than 1, as in the expression . You can write the exponent as a product in two different ways. Power of a Power Property Definition of

Example : Simplifying Expressions with Fractional Exponents B. Definition of = 243 = 25

Example Simplify each expression. a. b. Definition of = (1)3 = 8 = 1

Example Simplify each expression. c. Definition of = 81

Example: Properties of Exponents to Simplify Expressions Definition of Power of a Product Property • Power of a Power Property Simplify exponents.

Example: Properties of Exponents to Simplify Expressions • Power of a Product Property Simplify exponents. Product of Powers Property

Check It Out! Simplify. All variables represent nonnegative numbers. Definition of Power of a Product Property Simplify exponents.

Check It Out! Simplify. All variables represent nonnegative numbers. Definition of Power of a Product Property Simplify exponents.

Lesson Quiz: Part I Simplify each expression. 1. 2. 3. 4.

Lesson Quiz: Part II Simplify. All variables represent nonnegative numbers. 5. 6.