Well, yes and no. In general, with nonlinear regression, the residual mean at the minimum may not be zero, which is assumed by the usual calculation, so this can throw things off a lot.
However, with your example, I wonder whether you really meant a to be both the intercept and the coefficient of the exponent. That would be very unusual and might cause estimation to fail.
If those two should really be different parameters, then the model isn't essentially nonlinear. You could take the log of both sides and estimate it as an ordinary linear model. In its current form, you could either use Curve Fit or nonlinear regression to estimate it.
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