Section 4.2 Rational Exponents

Definition of Rational Exponents Introduction How should we define , n is a counting number? Exponent property is true if m = ½ n = 2 (–3)2 = 9 and 32 = 9 Suggests that 9½ = 3 The nonnegative number 3 is the principal second root, or principle square root, of 9, written If m = , n = 3: Section 4.2 Slide 2

Definition of Rational Exponents Introduction 23 = 8 Suggests that a good meaning of is 2 The number 2 is called the third root, or cube root, of 8 written Section 4.2 Slide 3

Definition of Rational Exponents For the counting number n, where n ≠ 1, If n is odd, then is the number whose nth power is b, and we call the nth root of b. If n is even and , then is the nonnegative number whose nth power is b, and we call the principle square root of b. If n is even and b < 0, then is not a real number may be represented by Section 4.2 Slide 4

Example Solution Simplifying Expressions Involving Rational Exponents Definition of Rational Exponents Example Simplify. Solution Section 4.2 Slide 5

Simplifying Expressions Involving Rational Exponents Definition of Rational Exponents Solution Continued is not a real number, since the fourth power of any real number is nonnegative. Graphing calculator checks problems 1, 2 and 3 Section 4.2 Slide 6

Definition: Rational Exponent Definition of Rational Exponents Definition For the counting numbers m and n, where n ≠ 1 and b is any real number for which is a real number, A power of the form or is said to have a rational exponent. Section 4.2 Slide 7

Example Solution Simplifying Expressions Involving Rational Exponents Definition of Rational Exponents Example Simplify. Solution Section 4.2 Slide 8

Graphing calculator checks problems 1, 2 and 3 Simplifying Expressions Involving Rational Exponents Definition of Rational Exponents Solution Continued Graphing calculator checks problems 1, 2 and 3 Section 4.2 Slide 9

For find the following: Simplifying Expressions Involving Rational Exponents Definition of Rational Exponents Example For find the following: Solution Section 4.2 Slide 10

Solution Continued Properties Simplifying Expressions Involving Rational Exponents Definition of Rational Exponents Solution Continued If m and n are real rational numbers and b and c are any real number for which bm, bn and cn are real numbers Properties Section 4.2 Slide 11

Properties of Rational Exponents Properties Continued Section 4.2 Slide 12