# E raised to a power with units

#### bluestar

When e is raised to a power with units of mass what is the units of the resulting solution?

#### Hurkyl

Staff Emeritus
Gold Member
e^{mass}. But more likely, there's a constant missing from your formula.

#### neutrino

It can never be done that way. e, or any other constant, can only be raised to a dimensionless quantity. So, if you find a mass term in the exponent, there must also be one or more terms together having a dimension of M-1, and vice versa.

#### Hootenanny

Staff Emeritus
Gold Member
When e is raised to a power with units of mass what is the units of the resulting solution?
In dimensional analysis, the argument of an exponential must be dimensionless. In other words the argument of an exponential cannot have any units associated with it.

Edit: I see that I have been beaten to it.

#### bluestar

I have simplified the example because the actual formula has e raised to multiple units. I thought if I could understand how a single unit is handled then I could figure out all of the units would be handled in the actual formula.

The unit mass is associated with a numerical value so e^mass can be computed. I just don’t understand what the units would be after the calculation.

#### Hurkyl

Staff Emeritus
Gold Member
I have simplified the example because the actual formula has e raised to multiple units.
What, praty tell, is the unit on the exponent (in its entirety)?

#### bluestar

I have been working in kg, Js, and meter, seconds. I think I can change kg into eV and then into Js and perhaps I can arrive at a unitless exponent.

Thanks for the guidance.
RON