How power and exponential are related?

Question

I have a model to fit but I am not sure if it is correct:

Is $\exp(ax+bz+c)^d$ algebraically the same as $\exp(dax+dbz+dc)$?

Edit

what about this one?

Is $[exp(ax+bz+c)+j]^d$ algebraically the same as as $[exp(dax+dbz+dc)+dj]$

Where a,b,c,j,d are parameters for non-linear regression fit.

If so, why? Can you explain please?

It would help to have more parentheses there: both $(\exp(x))^d$ and $\exp(x^d)$ are unambiguous, while $\exp(x)^d$ is something that will make the reader wonder about the intended meaning. — , Mar 11 '15 at 00:07

score 0 · Accepted Answer · answered Mar 10 '15 at 21:42

0

Yes, it is correct. Note that $\exp(z) = e^z$, where $e$ is a number given by $e = 2.71828...$. It then follows from a basic property of exponents that $$ \exp(ax + bz + c)^d = \\ \left[e^{ax+bz+c}\right]^d =\\ e^{(ax+bz+c)d} =\\ e^{dax + dbz + dc} =\\ \exp(dax + dbz + dc) $$

answered Mar 10 '15 at 21:42

Ben Grossmann

225,327

Thanks.I edited my question would you please have a look. – Barry Mar 11 '15 at 08:41
The answer to that one is no, for the same reason. – Ben Grossmann Mar 11 '15 at 11:04

How power and exponential are related?

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