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

2. Objective
Evaluate and simplify expressions containing rational exponents.

5. 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
= = 5

6. 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 =
= 15

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

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

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

10. 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.

11. 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

12. 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.

13. 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

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

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

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

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

18. 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.