Rational Exponents

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Rational Exponent (an exponent expressed as a ratio):

x^a/b = (x^1/b)^a = (^b√ x )^a

EXAMPLE:

4^1/2 = √ 4  = 2

8^1/3 = ³√ 8  = 2

8^2/3 = (8^1/3)² = (³√ 8 )² = 4

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

9^1/2 = √ 9  = 3

16^1/2 = √ 16  = 4

25^1/2 = √ 25  = 5

36^1/2 = √ 36  = 6

49^1/2 = √ 49  = 7

4^1/3 = ³√ 4 

8^1/3 = ³√ 8  = 2

16^1/3 = ³√ 16  = ³√ 8  × ³√ 2  = 2 ³√ 2 

2^2/3 = (2^1/3)² = (³√ 2 )²

8^2/3 = (8^1/3)² = (³√ 8 )² = 2² = 4

27^2/3 = (27^1/3)² = (³√ 27 )² = 3² = 9

• 4^1/2 =
  2
• 9^1/2 =
  3
• 16^1/2 =
  4
• 25^1/2 =
  5
• 36^1/2 =
  6
• 49^1/2 =
  7
• 8^1/3 =
  2
• 8^2/3 =
  4
• 27^1/3 =
  3
• 27^2/3 =
  9
• 64^1/3 =
  4
• 64^2/3 =
  16
• 125^1/3 =
  5
• 125^2/3 =
  25
• 216^1/3 =
  6
• 216^2/3 =
  36
• 343^1/3 =
  7
• 343^2/3 =
  49
• 512^1/3 =
  8
• 512^2/3 =
  64
• 729^1/3 =
  9
• 729^2/3 =
  81
• 1000^1/3 =
  10
• 1000^2/3 =
  100
• 8^4/3 =
  2⁴ = 16
• 16^5/4 =
  2⁵ = 32
• 3^4/2 =
  3² = 9
• 2^6/2 =
  2³ = 8
• 4^6/3 =
  4² = 16
• 2^9/3 =
  2³ = 8
• 2^27/3 =
  2⁹ = 512
• 4^27/9 =
  4³ = 64