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