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Published byAnderson Westley Modified over 2 years ago

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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 b. Because n = 4 is even and a = 81 > 0, 81 has two real fourth roots. Because 3 4 = 81 and (–3) 4 = 81, you can write ± 4 81 = ±3 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 2 Evaluate expressions with rational exponents Evaluate (a) 16 3/2 and (b) 32 –3/5. SOLUTION Rational Exponent Form Radical Form a. 16 3/2 (16 1/2 ) 3 = 4343 = 64 = 16 3/2 ( ) 3 = = 64= b. 32 –3/5 = /5 = 1 (32 1/5 ) 3 = = 32 –3/ /5 = 1 ( ) = = =

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EXAMPLE 3 Approximate roots with a calculator Expression Keystrokes Display a. 9 1/ b. 12 3/ c. ( 4 ) 3 = 7 3/

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

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GUIDED PRACTICE for Examples 1, 2 and 3 Evaluate expressions without using a calculator /2 SOLUTION –1/2 SOLUTION /4 SOLUTION /8 SOLUTION 1

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GUIDED PRACTICE for Examples 1, 2 and 3 Evaluate the expression using a calculator. Round the result to two decimal places when appropriate. Expression / /3 – 11. ( 4 16) ( 3 –30) 2 SOLUTION

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