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Properties of Rational Exponents

Properties of Rational Exponents. Section 7.2. What You Will Learn:. 1. Simplify expressions with rational exponents. 2. Use properties of rational exponents. 3. Write an expression involving rational exponents in simplest form. 4. Perform operations with rational exponents.

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Properties of Rational Exponents

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  1. Properties of Rational Exponents • Section 7.2

  2. What You Will Learn: 1. Simplify expressions with rational exponents. 2. Use properties of rational exponents. 3. Write an expression involving rational exponents in simplest form. 4. Perform operations with rational exponents. 5. Simplify expressions that have variables and rational exponents. 6. Write an expression involving variables and rational exponents in simplest form. 7. Perform operations with rational exponents and variables.

  3. Properties of Rational Exponents: Property: Example: 1. 2. (am)n = amn 3. (ab)m = ambm 4. Properties of Rational Exponents

  4. Properties of Rational Exponents: Property: Example: 5. 6. Properties of Rational Exponents (cont.)

  5. Simplify the expressions: 1. 2. 3. Using the Properties

  6. 4. 5. More Fun with Properties

  7. Simplify: 1. 2. 3. 4. 5. You Try

  8. Simplify the expressions: 1. 2. More Simplifying

  9. Simplify: 1. 2. You Try

  10. In order for a radical to be in simplest form, you have to remove any perfect nth powers and rationalize denominators. Example: Write in simplest form: 1. 2. Simplest Form - continued

  11. Write in simplest form: 1. 2. You Try

  12. Two radicals expressions are “like radicals” if they have the same index and the same radicand. Example: Perform the indicated operation: 1. 2. Operations Using Radicals

  13. Perform the indicated operation: 1. 2. You Try

  14. Important! = x when n is odd. = |x| when n is even. Simplifying Expressions Involving Variables

  15. Simplify the expression. Assume all variables are positive: 1. 2. 3. 4. Simplifying

  16. Simplify the expression. Assume all variables are positive. 1. 2. 3. 4. You Try

  17. Write the expression in simplest form. Assume all variables are positive. 1. 2. Writing Variable Expressions in Simplest Form

  18. Write the expression in simplest form. Assume all variables are positive. 1. 2. You Try

  19. Perform the indicated operation. Assume all variables are positive. 1. 2. 3. Adding and Subtracting Expressions Involving Variables

  20. Perform the indicated operations. Assume all variables are positive. 1. 2. 3. You Try

  21. Homework • page 411, 22-30 even, 34-62 even, 66-72 even, 76, 80 • :

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