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EXAMPLE 1

a. Because n = 3 is odd and a = –216 < 0, –216 has one real cube root. Because (–6) 3 = –216 , you can write = 3 √ –216 = –6 or (–216) 1/3 = –6.

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EXAMPLE 1

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  1. a. Because n = 3 is odd and a = –216 < 0, –216 has one real cube root. Because (–6)3= –216, you can write = 3√–216 = –6 or (–216)1/3 = –6. b. Because n = 4 is even and a = 81 > 0, 81 has two real fourth roots. Because 34 = 81 and (–3)4 = 81, you can write ±4√ 81 =±3 EXAMPLE 1 Find nth roots Find the indicated real nth root(s) of a. a. n = 3, a = –216 b. n = 4, a = 81 SOLUTION

  2. 1 1 23 323/5 64 ( )3 = (161/2)3 = 43 = 43 = 64 = = 16  1 1 1 1 1 1 = = = = ( )3 (321/5)3 323/5 32  5 8 23 8 = = = = EXAMPLE 2 Evaluate expressions with rational exponents Evaluate (a) 163/2 and (b)32–3/5. SOLUTION Radical Form Rational Exponent Form a. 163/2 163/2 b. 32–3/5 32–3/5

  3. Keystrokes Expression Display 9 1 5 7 3 4 12 3 8 7  c. ( 4 )3 = 73/4 EXAMPLE 3 Approximate roots with a calculator a. 91/5 1.551845574 b. 123/8 2.539176951 4.303517071

  4. for Examples 1, 2 and 3 GUIDED PRACTICE Find the indicated real nth root(s) of a. 1. n = 4, a = 625 3. n = 3, a = –64. SOLUTION ±5 SOLUTION –4 2.n = 6, a = 64 4. n = 5, a = 243 SOLUTION ±2 SOLUTION 3

  5. 1 3 for Examples 1, 2 and 3 GUIDED PRACTICE Evaluate expressions without using a calculator. 5. 45/2 7. 813/4 27 SOLUTION 32 SOLUTION 6. 9–1/2 8. 17/8 SOLUTION SOLUTION 1

  6. Expression 10. 64 2/3 – 11. (4√ 16)5 12. (3√–30)2 for Examples 1, 2 and 3 GUIDED PRACTICE Evaluate the expression using a calculator. Round the result to two decimal places when appropriate. 9. 42/5 1.74 SOLUTION SOLUTION 0.06 SOLUTION 32 9.65 SOLUTION

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