Review of Introductory Mathematics EXPONENTS Fractional Exponents Fractional  exponents  are  defined  as  follows, .    This  permits  manipulations  with a 1 m n a numbers with fractional exponents to be treated using the laws expressed earlier for integers.  For example, 8 1 3 3 8 2 since  2×2×2 8 Taking  the  statement and  cubing  both  sides, .    But  (a^m)ⁿ  =  a m  x  n so 8 1 3 2 8 1 3 3 2³ which agrees with 2³ = 8 for the right-hand side of the equality. 8 1 3 3 8¹ 8 A number such as can be written or alternately as since 8 2 3 8 1 3 2 2² 4 8² 1 3 64 1 3 4 4 x 4 x 4 = 64; that is, 4 is the cube root of 64. Examples: a 1 3 a 2 3 a 1 3 2 3 a¹ a b 1 4 b 1 2 b 1 4 1 2 b 1 2 1 b² d 1 3 9 d 1 3 ×9 d³ Rev. 0 Page 65 MA-01