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Properties of Rational Exponents

Properties of Rational Exponents. Section 6.2. 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 6.2

  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. f.

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

  7. 4. 5. More Fun with Properties

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

  9. Write the expression in simplest form You need to rationalize the denominator—no tents in the basement

  10. Adding and subtracting like radicals and root. • When adding or subtracting like radicals the root and the number under the radical sign must be the same before you can add or subtract coefficients. • Radical expressions with the same index and radicand are like radicals. • You may need to simplify the radical before you can add or subtract.

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

  12. Simplify: 1. 2. You Try

  13. 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

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

  15. 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

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

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

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

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

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

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

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

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

  24. Do properties of exponents work for roots? Same rules apply. What form must radical be in? Fractional exponent form How do you know when a radical is in simplest form? When there are no more numbers to the root power as factors of the number under the radical. Before you can add or subtract radicals what must be true? The number under the radicals must be the same.

  25. Assignments • Class Work – Page 424-426 [#s 3-65 Odds; 66-68 All; 69-81 Odds; 83-84.] • Home Work: Worksheet 6.2 ALL – Due Thursday • Quiz 6.1-6.2-6.3 THURSDAY MAY 8th

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