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Ch. 7.4 Rational Exponents

This lesson explains how to simplify expressions with rational exponents and convert between radical and exponential forms. Includes practice problems and check understanding questions.

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Ch. 7.4 Rational Exponents

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  1. Ch. 7.4 Rational Exponents p. 379

  2. Rational Exponents • If the nth root of a is a real number and m is an integer, then: and If m is negative, a ≠ 0

  3. 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. Rational Exponents ALGEBRA 2 LESSON 7-4 Simplify each expression. = 4 Definition of cube root. 7-4

  4. 1 3 1 3 c. 5 • 25 1 3 1 3 5 • 25 = 5 • 25 Rewrite as radicals. 3 3 3 = 5 • 25 property for multiplying radical expressions 3 = 5 By definition, 5 is the number whose cube is 5. Rational Exponents ALGEBRA 2 LESSON 7-4 (continued) 7-4

  5. Check Understanding • P. 379 Check understanding # 1 A - C

  6. Properties of Rational Exponents Let m and n represent rational numbers. Assume that no denominator equals 0. Property Example

  7. Properties of Rational Exponents Continued Property Example

  8. 2 5 – 2 7 1 y 2 a. Write x and y –0.4 in radical form. 5 7 7 1 y2 2 7 x = x2 or x2 y –0.4 = y = or 5 b. Write the radical expressions and in exponential form. 3 4 = c c3 c3 4 4 5 3 = b b 5 b 5 3 3 Rational Exponents ALGEBRA 2 LESSON 7-4 7-4

  9. Check Understanding • p. 380, Check Understanding 2 A & B

  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 Rational Exponents ALGEBRA 2 LESSON 7-4 Simplify each number. 7-4

  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 = Rational Exponents ALGEBRA 2 LESSON 7-4 (continued) b. 25–2.5 7-4

  12. Check Understanding • P. 381, Check understanding #4 A - C

  13. 2 5 2 5 (243a–10) = (35a–10) = 35 • a(–10) 2 5 2 5 32 a4 9 a4 = = Rational Exponents ALGEBRA 2 LESSON 7-4 Write (243a–10) in simplest form. 2 5 = 32a–4 7-4

  14. Check Understanding • P. 382, Check Understanding # 5

  15. Homework • Page 382 # 2 – 22 eoe, 30 – 60 eoe

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