# What is the degree of e^(y/x)?

### 7 Answers

- TomVLv 76 months ago
The concept of degree of an expression is only applicable to polynomials.

The expression e^(y/x) is not a polynomial.

The expression has no degree.

The question is analogous to asking the color of anger.

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- Demiurge42Lv 76 months ago
Only polynomials have a degree. e^(y/x) isn't a polynomial.

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- KrishnamurthyLv 76 months ago
The degree of e^(y/x) is (y/x).

- 無Lv 46 months agoReport
good answer, also, : x such that x≠0 etc

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- JOHNLv 76 months ago
The degree of y/x is deg (y) - deg (x) = 1 - 1 = 0.

e^(y/x) is a function of y/x and has degree 0.

An illustration from physics might help clarify this.

Dimensionally, whenever the exponential appears

in a physical equation, the argument of the

exponential must be a dimensionless pure number,

or else the expression doesn't make sense and can't

be a term of a true equation. For instance Planck's

radiation law states E(ν) = hν/[e^(hν/kT) - 1]. Now

[hν] = [joules] and [ kT] = [joules] (k = Boltzmann's

constant, T = Kelvin temperperature). so we have

joules/joules = pure number and e^(hν/kT) makes

sense. Further, on te left of the radiation law we

have joules and on the right we have joules/pure

number = joules. Thus the hν/kT of e^(hν/kT) has

to be a pure number for all to make sense.

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