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7-4 Rational Exponents

7-4 Rational Exponents. Objectives. Simplifying Expressions w/ Rational Exponents. Vocabulary. Another way to write a radical expression is to use a rational exponent. =. =. =. 1 3. a. 64. 1 3. 64 = 64 Rewrite as a radical. 3. 3. = 4 3 Rewrite 64 as a cube. 1 2. 1 2.

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7-4 Rational Exponents

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  1. 7-4 Rational Exponents

  2. Objectives Simplifying Expressions w/ Rational Exponents

  3. Vocabulary Another way to write a radical expression is to use a rational exponent. = = =

  4. 1 3 a. 64 1 3 64 = 64 Rewrite as a radical. 3 3 = 43Rewrite 64 as a cube. 1 2 1 2 b. 7 • 7 1 2 1 2 7 • 7 = 7 • 7 Rewrite as radicals. = 7 By definition, 7 is the number whose square is 7. Simplifying Expressions w/ Rational Exponents Simplify each expression. = 4 Definition of cube root.

  5. 1 3 1 3 c. 5 • 25 3 = 5 • 25 property for multiplying radical expressions 3 = 5 By definition, 5 is the number whose cube is 5. Continued (continued) 1 3 1 3 5 • 25 = 5 • 25 Rewrite as radicals. 3 3

  6. Vocabulary Rational Exponents

  7. 1 1 y 2 2 7 2 5 y –0.4 = y = or – 7 x = x2 or x2 7 5 y2 5 5 3 3 4 4 3 c3 b 5 = b = c Converting To and From Radical Form 2 7 a. Write the exponential expressions x and y –0.4 in radical form. 3 4 b. Write the radical expressions and in exponential form. b 5 c3

  8. 4.15 Use a calculator. Real World Example The time t in hours needed to cook a pot roast that weighs p pounds can be approximated by using the equation t = 0.89p0.6. To the nearest hundredth of an hour, how long would it take to cook a pot roast that weighs 13 pounds? t = 0.89p0.6Write the formula. = 0.89(13)0.6Substitute for p. It would take 4.15 hours to cook a 13 pound pot roast.

  9. Vocabulary Properties of Rational Exponents

  10. 2 3 a. (–27) Method 1 Method 2 2 3 (–27) = ( –27)2 3 2 3 2 3 (–27) = ((–3)3) = ( (–3)3)2 3 = (–3)2 = 9 = (–3)2 = 9 Simplifying Numbers w/ Rational Exponents Simplify each number.

  11. Method 1 Method 2 5 2 – 25–2.5 = 25 25–2.5 = 25 = (52) 1 = 5 2 25 = 5–5 5 2 5 2 5 2 – – – 1 ( 25)5 = 1 55 = 1 3125 1 3125 = = 1 55 = 52 = Continued (continued) b. 25–2.5

  12. 2 5 2 5 (243a–10) = (35a–10) = 35 • a(–10) 2 5 2 5 32 a4 9 a4 = = Writing Expressions in Simplest Form Write (243a–10) in simplest form. 2 5 = 32a–4

  13. Homework Pg 388 & 389 #1, 2, 10, 11, 30, 31, 38, 39

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