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7.3 nth Roots and Rational Exponents

7.3 nth Roots and Rational Exponents. ©2001 by R. Villar All Rights Reserved. nth Roots and Rational Exponents. You know that 3 is the square root of 9 because 9 is “ 3 squared ” Roots exist other than “square” roots. Consider the following...

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7.3 nth Roots and Rational Exponents

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  1. 7.3 nth Roots and Rational Exponents ©2001 by R. Villar All Rights Reserved

  2. nth Roots and Rational Exponents You know that 3 is the square root of 9 because 9 is “3 squared” Roots exist other than “square” roots. Consider the following... 2 is the cube root of 8 since 23 = 8 5 is a fourth root of 625 since 54 = 625 –5 is a fourth root of 625 since (–5)4 = 625 These roots can be written with two different types of notation…Radical Notation or Rational Exponent Notation These are both asking for the third (or cube) root of 8... …which is 2 since 23 = 8

  3. Examples: =4 Simplify: 625 –1/4 This is the same as 1 625 1/4 or Simplify: 641/3 This is the same as (43)1/3 =4 or641/3 = ± 1 5

  4. To simplify rational exponents, you may use the following: am/n = (a1/n)m Example: Simplify 82/3 = (81/3)2 = (2)2 = 4 Example: Simplify 64-2/3 = (641/3)-2 = (4)-2 = 1 (4)2 = 1 16

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