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

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

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

4. 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 .

5. 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,

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

8. 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

9. 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

10. 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

12. Example : Simplifying Expressions with Fractional ExponentsB.
Definition of
= 243
= 25

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

14. Example
Simplify each expression. c.
Definition of
= 81

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

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

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

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

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

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