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

Objective Evaluate and simplify expressions containing rational exponents.

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

Additional Example 2: Simplifying Expressions with Fractional Exponents Simplify each expression. A. B. Definition of = 243 = 25

Check It Out! Example 2 Simplify each expression. a. b. Definition of = (1)3 = 8 = 1

Check It Out! Example 2 Simplify each expression. c. Definition of = 81

Additional Example 3: Application Given a cube with surface area S, the volume V of the cube can be found by using the formula Find the volume of a cube with surface area 54 m2. Substitute 54 for s. Simplify inside the parentheses. Definition of The volume of the cube is 27 m3.

The approximate number of Calories C that an Check It Out! Example 3 The approximate number of Calories C that an 2 animal needs each day is given by , where m is the animal’s mass in kilograms. Find the number of Calories that an 81 kg panda needs each day. Substitute 81 for m. Definition of The panda needs 1944 Calories per day to maintain health. = 7227 = 1944

Additional Example 4A: Properties of Exponents to Simplify Expressions Simplify. All variables represent nonnegative numbers. Definition of Power of a Product Property • Power of a Power Property Simplify exponents.

Additional Example 4B: Properties of Exponents to Simplify Expressions Simplify. All variables represent nonnegative numbers. • Power of a Product Property Simplify exponents. Product of Powers Property

Check It Out! Example 4a Simplify. All variables represent nonnegative numbers. Definition of Power of a Product Property Simplify exponents.

Check It Out! Example 4a Simplify. All variables represent nonnegative numbers. Definition of Power of a Product Property Simplify exponents.

Check It Out! Example 4b Simplify. All variables represent nonnegative numbers. Power of a Product Property and Simplify. = xy

Lesson Quiz: Part I Simplify each expression. 1. 2. 3. 4. 2 9 729 128

Lesson Quiz: Part II 5. In an experiment, the approximate population P of a bacteria colony is given by , where t is the number of days since start of the experiment. Find the population of the colony on the 8th day. 480 Simplify. All variables represent nonnegative numbers. 6. 7.