Roots, Radicals, and Root Functions 7 Chapter Roots, Radicals, and Root Functions

7.2 Rational Exponents 1. Use exponential notation for nth roots. 2. Define and use expressions of the form am/n. 3. Convert between radicals and rational exponents. 4. Use the rules for exponents with rational exponents.

Use exponential notation for nth roots. Objective 1 Use exponential notation for nth roots.

Use exponential notation for nth roots.

Evaluating Exponentials of the Form a1/n Classroom Example 1 Evaluating Exponentials of the Form a1/n Evaluate each exponential. a. 321/5 b. 641/2 c. –811/4 d. (–81)1/4 It is not a real number, because the radicand is negative and the index is even.

Define and use expressions of the form am/n. Objective 2 Define and use expressions of the form am/n.

Define and use expressions of the form am/n.

Evaluating Exponentials of the Form am/n Classroom Example 2 Evaluating Exponentials of the Form am/n Evaluate each exponential. a. 253/2 b. 272/3 c. –163/2 d. (–64)2/3 e. (–36)3/2 Not a real number

Define and use expressions of the form am/n.

Evaluating Exponentials of the Form a–m/n Classroom Example 3 Evaluating Exponentials of the Form a–m/n Evaluate each exponential. a. b. c.

Define and use expressions of the form am/n.

Convert between radicals and rational exponents. Objective 3 Convert between radicals and rational exponents.

Converting between Rational Exponents and Radicals Classroom Example 4 Converting between Rational Exponents and Radicals Write each exponential as a radical. Assume that all variables represent positive real numbers. a. 191/2 b. 113/4 c. 14x2/3 d.

Converting between Rational Exponents and Radicals (cont.) Classroom Example 4 Converting between Rational Exponents and Radicals (cont.) Write each radical as an exponential. Simplify. Assume that all variables represent positive real numbers. g. h. i.

Use the rules for exponents with rational exponents. Objective 4 Use the rules for exponents with rational exponents.

Rules for Rational Exponents

Applying Rules for Rational Exponents Classroom Example 5 Applying Rules for Rational Exponents Simplify each expression. Write answers with only positive exponents. Assume that all variables represent positive real numbers. a. b. c.

Applying Rules for Rational Exponents (cont.) Classroom Example 5 Applying Rules for Rational Exponents (cont.) Simplify each expression. Write answers with only positive exponents. Assume that all variables represent positive real numbers. d.

Applying Rules for Rational Exponents (cont.) Classroom Example 5 Applying Rules for Rational Exponents (cont.) Simplify each expression. Write answers with only positive exponents. Assume that all variables represent positive real numbers. e.

Applying Rules for Rational Exponents Classroom Example 6 Applying Rules for Rational Exponents Write each radical as an exponential, and then simplify. Leave answers in exponential form. Assume that all variables represent positive real numbers. a. b. c.