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§ 7.2

§ 7.2. Rational Exponents. Rational Exponents. P 499. Blitzer, Intermediate Algebra , 5e – Slide # 2 Section 7.2. Rational Exponents. EXAMPLE. Use radical notation to rewrite each expression. Simplify, if possible:. SOLUTION.

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§ 7.2

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  1. §7.2 Rational Exponents

  2. Rational Exponents P 499 Blitzer, Intermediate Algebra, 5e – Slide #2 Section 7.2

  3. Rational Exponents EXAMPLE Use radical notation to rewrite each expression. Simplify, if possible: SOLUTION Blitzer, Intermediate Algebra, 5e – Slide #3 Section 7.2

  4. Rational Exponents Check Point 1 on page 499 Blitzer, Intermediate Algebra, 5e – Slide #4 Section 7.2

  5. Rational Exponents EXAMPLE Rewrite with rational exponents: SOLUTION Parentheses are needed in part (a) to show that the entire radicand becomes the base. Blitzer, Intermediate Algebra, 5e – Slide #5 Section 7.2

  6. Rational Exponents Check Point 2 on p 500 Blitzer, Intermediate Algebra, 5e – Slide #6 Section 7.2

  7. Rational Exponents Blitzer, Intermediate Algebra, 5e – Slide #7 Section 7.2

  8. Rational Exponents EXAMPLE Use radical notation to rewrite each expression and simplify: SOLUTION Blitzer, Intermediate Algebra, 5e – Slide #8 Section 7.2

  9. Rational Exponents Check Point 3 on p 501 Blitzer, Intermediate Algebra, 5e – Slide #9 Section 7.2

  10. Rational Exponents EXAMPLE Rewrite with rational exponents: SOLUTION Blitzer, Intermediate Algebra, 5e – Slide #10 Section 7.2

  11. Rational Exponents Check Point 4 on p 501 Blitzer, Intermediate Algebra, 5e – Slide #11 Section 7.2

  12. Rational Exponents Blitzer, Intermediate Algebra, 5e – Slide #12 Section 7.2

  13. Rational Exponents Check Point 5 on p 502 Blitzer, Intermediate Algebra, 5e – Slide #13 Section 7.2

  14. Rational Exponents in Application EXAMPLE The Galapagos Islands, lying 600 miles west of Ecuador, are famed for their extraordinary wildlife. The function models the number of plant species, f(x), on the various islands of the Galapagos chain in terms of the area, x, in square miles, of a particular island. Use the function to solve the following problem. How many species of plants are on a Galapagos island that has an area of 27 square miles? Blitzer, Intermediate Algebra, 5e – Slide #14 Section 7.2

  15. Rational Exponents in Application CONTINUED SOLUTION Because we are interested in how many species of plants there are on a Galapagos island having an area of 27 square miles, substitute 27 for x. Then calculate f(x). This is the given formula. Replace x with 27. Rewrite as . Evaluate the cube root. Multiply. A Galapagos island having an area of 27 square miles contains approximately 87 plant species. Blitzer, Intermediate Algebra, 5e – Slide #15 Section 7.2

  16. Rational Exponents p 502 Blitzer, Intermediate Algebra, 5e – Slide #16 Section 7.2

  17. Rational Exponents p 502 CONTINUED Blitzer, Intermediate Algebra, 5e – Slide #17 Section 7.2

  18. Rational Exponents EXAMPLE Simplify: SOLUTION To divide with the same base, subtract exponents. Subtract. Blitzer, Intermediate Algebra, 5e – Slide #18 Section 7.2

  19. Rational Exponents CONTINUED To raise a product to a power, raise each factor to the power. Multiply: Rewrite with positive exponents. Blitzer, Intermediate Algebra, 5e – Slide #19 Section 7.2

  20. Rational Exponents Check Point 6 on page 503 Simplify: Blitzer, Intermediate Algebra, 5e – Slide #20 Section 7.2

  21. Rational Exponents Blitzer, Intermediate Algebra, 5e – Slide #21 Section 7.2

  22. Rational Exponents EXAMPLE Use rational exponents to simplify: SOLUTION Rewrite as exponential expressions. Raise each factor in parentheses to its related power. To raise powers to powers, multiply. Reorder the factors. To multiply with the same base, add exponents. Blitzer, Intermediate Algebra, 5e – Slide #22 Section 7.2

  23. Rational Exponents Add. CONTINUED Rewrite exponents with common denominators. Factor 1/6 out of the exponents. Rewrite in radical notation. Write the radicand as an exponential expression. Write the entire expression in exponential form. To raise powers to powers, multiply the exponents. Rewrite in radical notation. Blitzer, Intermediate Algebra, 5e – Slide #23 Section 7.2

  24. Rational Exponents Important to Remember: • An expression with rational exponents is simplified • when no parentheses appear, • no powers are raised to powers, • each base occurs once, and • no negative or zero exponents appear. • Some radical expressions can be simplified using rational exponents. Rewrite the expression using rational exponents, simplify, and rewrite in radical notation if rational exponents still appear. Blitzer, Intermediate Algebra, 5e – Slide #24 Section 7.2

  25. DONE

  26. Rational Exponents Rational exponents have been defined in such a way so as to make their properties the same as the properties for integer exponents. In this section we explore the meaning of a base raised to a rational (fractional) exponent. We will also discover how we can use rational exponents to simplify radical expressions. Blitzer, Intermediate Algebra, 5e – Slide #26 Section 7.2

  27. Rational Exponents Important to Remember: Blitzer, Intermediate Algebra, 5e – Slide #27 Section 7.2

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