Rational Exponents

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Rational Exponent (an exponent expressed as a ratio):

xa/b = (x1/b)a = (b x )a

EXAMPLE:

41/2 =  4  = 2

81/3 = 3 8  = 2

82/3 = (81/3)2 = (3 8 )2 = 4

Use this extended list of examples for practice; then try your brain on the flashcards.

91/2 =  9  = 3

161/2 =  16  = 4

251/2 =  25  = 5

361/2 =  36  = 6

491/2 =  49  = 7

41/3 = 3 4 

81/3 = 3 8  = 2

161/3 = 3 16  = 3 8  × 3 2  = 2 3 2 

22/3 = (21/3)2 = (3 2 )2

82/3 = (81/3)2 = (3 8 )2 = 22 = 4

272/3 = (271/3)2 = (3 27 )2 = 32 = 9

  • 41/2 =
    2
  • 91/2 =
    3
  • 161/2 =
    4
  • 251/2 =
    5
  • 361/2 =
    6
  • 491/2 =
    7
  • 81/3 =
    2
  • 82/3 =
    4
  • 271/3 =
    3
  • 272/3 =
    9
  • 641/3 =
    4
  • 642/3 =
    16
  • 1251/3 =
    5
  • 1252/3 =
    25
  • 2161/3 =
    6
  • 2162/3 =
    36
  • 3431/3 =
    7
  • 3432/3 =
    49
  • 5121/3 =
    8
  • 5122/3 =
    64
  • 7291/3 =
    9
  • 7292/3 =
    81
  • 10001/3 =
    10
  • 10002/3 =
    100
  • 84/3 =
    24 = 16
  • 165/4 =
    25 = 32
  • 34/2 =
    32 = 9
  • 26/2 =
    23 = 8
  • 46/3 =
    42 = 16
  • 29/3 =
    23 = 8
  • 227/3 =
    29 = 512
  • 427/9 =
    43 = 64