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