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 Warm Up Simplify each expression. 1. 2. 3. 4. Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Essential Question How do you evaluate and simplify expressions containing rational exponents? Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Recall that the radical symbol roots. is used to indicate 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. Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Another way to write nth roots is by using fractional exponents. For example, for b >1, suppose b 1 = b 2 k 1 = 2 k Square both sides. Power of a Power Property If bm = bn, then m = n. Divide both sides by 2. So for all b > 1, Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Helpful Hint When b = 0, When b = 1, 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 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 Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Holt Mc. Dougal Algebra 1

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

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

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

6 -2 Rational Exponents Example: Properties of Exponents to Simplify Expressions Definition of • Power of a Product Property Power of a Power Property Simplify exponents. Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Example: Properties of Exponents to Simplify Expressions • • Power of a Product Property Simplify exponents. Product of Powers Property Holt Mc. Dougal Algebra 1

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

6 -2 Rational Exponents Lesson Quiz: Part I Simplify each expression. 1. 2. 3. 4. Holt Mc. Dougal Algebra 1

6 -2 Rational Exponents Lesson Quiz: Part II Simplify. All variables represent nonnegative numbers. 5. 6. Holt Mc. Dougal Algebra 1