8 6 Radical Expressions and Rational Exponents 8
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8 -6 Radical Expressions and Rational Exponents 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 = ____ n a _____ is the radicand 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
8 -6 Radical Expressions and Rational Exponents 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
8 -6 Radical Expressions and Rational Exponents 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
8 -6 Radical Expressions and Rational Exponents Example 5: Simplifying Radical Expressions Simplify each expression. Assume that all variables are positive. A. B. C. D. E. 8. 6 Pg. 4
8 -6 Radical Expressions and Rational Exponents Example 5: Simplifying Radical Expressions Simplify each expression. Assume that all variables are positive. A. B. C. D. E. F. 8. 6 Pg. 5
