Associated Topics || Dr. Math Home || Search Dr. Math

### Fractional Exponents

```
Date: 03/11/99 at 18:06:19
From: Tom Judd, D.V.M.
Subject: Fractional Exponents

I am a veterinarian at a large goat farm and I am trying to figure
out the water consumption of the average goat.

One of the formulae that I have is 145 grams of water per kilogram of
bodyweight to the power of .75 (145g per  BW Kg^.75).

I cannot remember how fractional exponents work!

Our average goat weighs 77 Kg.

I think 77 kg ^.75 would be

(.75 X 77 kg) X (.75 X 77 Kg)
= (57.75 X 57.75)
= 3335.06

Have I figured this out correctly?

Thank you!
```

```
Date: 03/15/99 at 12:36:31
From: Doctor Mike
Subject: Re: Fractional Exponents

A fractional power relates to the expression of the power in numerator
and denominator form. You have 3/4 for the 0.75 decimal. Similarly,
0.5 is 1/2 and 0.3333333 is 1/3 and so on. If you represent the
fraction as n/d then x to the n/d power means the  d-th  root of
x to the power n.

Examples: If d is 2 then we deal with the 2nd root,
which is commonly referred to as the square root.
If d is 3 then we deal with the 3rd root,
which is commonly referred to as the cube root.
If d is 4 then we deal with the 4th root,
which you get by taking the square root twice.

So, for your example of 77 to the 3/4 power, you would first take 77
to the third power, take the square root of that, and then, take the
square root again. What we get is

SQRT( SQRT( 77*77*77 ) )
= SQRT( SQRT(  456533  ) )
= SQRT(     675.67226    )
= 25.993697

which is about 26. I think, though, that this is a good place to use
an 8-dollar pocket calculator. Just enter 77, then the y^x key (or
something similar), then 0.75, and finally the = key.

Your final answer is 145*25.993697 = 3769.086 grams = 3.769086 kg, or
a bit under 4 kilograms of water. Of course, I cannot speak for the
accuracy of the formula.

I hope this helps.

- Doctor Mike, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Exponents

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search