# Failure of dimensional analysis for a rule

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Hi,

I have a rule y=x^0.35. x has the dimension of mass. An error message showed up saying that the exponent must be an integer constant. How can I handle this situation as this rule is very important in my model?

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### Accepted Answer

Arthur Goldsipe
on 21 Sep 2023

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### More Answers (1)

Walter Roberson
on 21 Sep 2023

I am baffled about what unit (grams ^ 0.35) would be. Should that be interpreted as (grams ^ (35/100) so that the unit would be "the 100'th root of grams to the 35'th power" ? Or should it be interpreted as (grams ^ (7/20)) ? so that the unit would be "the 20'th root of grams to the 7'th power" ?

Mind you, I also struggle with the physical meaning of something like y = sqrt(x) when x is mass.

If this is a situation of "never mind the dimensional continuity for now, the math works out" then you are going to have to strip the units from the item, make the math transformation, and add units back to the result.

##### 3 Comments

Walter Roberson
on 22 Sep 2023

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