# Negative, Rational Exponents

Back to “Exponents” Page

Negative, Rational Exponent
(a negative exponent expressed as a ratio):

xa/b = 1 / (b x )a

EXAMPLE:

4-1/2 = 1 /  4  = 1/2

8-1/3 = 1 / 3 8  = 1/2

8-2/3 = 1 / (3 8 )2 = 1/4

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

9-1/2 = 1 /  9  = 1/3

16-1/2 = 1 /  16  = 1/4

25-1/2 = 1 /  25  = 1/5

36-1/2 = 1 /  36  = 1/6

49-1/2 = 1 /  49  = 1/7

4-1/3 = 1 / 3 4

8-1/3 = 1 / 3 8  = 1/2

8-2/3 = 1 / (3 8 )2 = 1/22 = 1/4

27-2/3 = 1 / (3 27 )2 = 1/32 = 1/9

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