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?
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 $$ \exp(ax + bz + c)^d = \\ \left[e^{ax+bz+c}\right]^d =\\ e^{(ax+bz+c)d} =\\ e^{dax + dbz + dc} =\\ \exp(dax + dbz + dc) $$