Example 1: Finding Real Roots 8-6 LEARNING GOALS 8.6.1 Rewrite radical expressions by using rational exponents. 8.6.2 Simplify and evaluate radical expressions and expressions containing rational exponents. The nth root of a real number a can be written as the radical expression: __________ is the index (plural: indices) * If the index is left blank it means the index = ________ __________ is the radicand n a Example 1: Finding Real Roots Find all real roots. A. sixth roots of 64 B. cube roots of –216 C. fourth roots of –1024 8.6 Pg. 1

Example 2: Writing Expressions in Radical Form Write the expression in radical form and simplify. Method 1 Evaluate the root first. Method 2 Evaluate the power first. Use a calculator. A __________ ____________is an exponent that can be expressed as . For example: Write the expression in radical form, and simplify. A. 64⅓ B. 45/2 C. 625¾ Example 3: Writing Expressions by Using Rational Exponents Write each expression by using rational exponents. A. B. 8.6 Pg. 2

Example 4: Simplifying Expressions with Rational Exponents Simplify each expression. Check with your calculator. A. B. C. D. E. F. Example 5: Simplifying Radical Expressions Simplify each expression. Assume that all variables are positive. A. B. C. D. E. F. 8.6 Pg. 3

Example 5: Simplifying Radical Expressions Simplify each expression. Assume that all variables are positive. A. B. C. D. E. 8.6 Pg. 4

Example 5: Simplifying Radical Expressions Simplify each expression. Assume that all variables are positive. A. B. C. D. E. F. 8.6 Pg. 5