Exponents 6 2 Rational Exponents Warm Up Lesson

Exponents 6 -2 Rational Exponents Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 Holt Mc. Dougal

6 -2 Rational Exponents Objective Evaluate and simplify expressions containing rational exponents. Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Additional Example 1: Simplifying b Simplify each expression. 1 n A. Use the definition of 1 b n. =7 B. Use the definition of =2+3=5 Holt Mc. Dougal Algebra 1 1 b n.

6 -2 Rational Exponents Check It Out! Example 1 Simplify each expression. a. Use the definition 1 of b n. =3 b. Use the definition of = 11 + 4 = 15 Holt Mc. Dougal Algebra 1 1 b n.

6 -2 Rational Exponents Additional Example 2: Simplifying Expressions with Fractional Exponents Simplify each expression. A. B. Definition of = 243 Holt Mc. Dougal Algebra 1 = 25

6 -2 Rational Exponents Check It Out! Example 2 Simplify each expression. a. b. Definition of = (1)3 =8 Holt Mc. Dougal Algebra 1 =1

6 -2 Rational Exponents Check It Out! Example 2 Simplify each expression. c. Definition of = 81 Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents 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 m 2. Substitute 54 for s. Simplify inside the parentheses. Definition of The volume of the cube is 27 m 3. Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents 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 = 72 27 = 1944 Holt Mc. Dougal Algebra 1 The panda needs 1944 Calories per day to maintain health.

6 -2 Rational Exponents Additional Example 4 A: 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. Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Additional Example 4 B: Properties of Exponents to Simplify Expressions Simplify. All variables represent nonnegative numbers. • • Power of a Product Property Simplify exponents. Product of Powers Property Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Check It Out! Example 4 a Simplify. All variables represent nonnegative numbers. Definition of Power of a Product Property Simplify exponents. Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Check It Out! Example 4 a Simplify. All variables represent nonnegative numbers. Definition of Power of a Product Property Simplify exponents. Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Check It Out! Example 4 b Simplify. All variables represent nonnegative numbers. Power of a Product Property and Simplify. = xy Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents 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 8 th day. 480 Simplify. All variables represent nonnegative numbers. 6. 7. Holt Mc. Dougal Algebra 1