There is so-called Power Transform technique in signal processing where the unresolved signal is sharpened by raising each data to a constant positive power. The example shown below is a sum of two Gaussians, $G_1$ and $G_2$ plotted against time. In order to resolve the peaks one can apply a power of 5 to each data point. The result is the resolved pair as shown in the bottom figure.
The above operating is equivalent to raising the sum of Gaussians $G_1$ and $G_2$ to the power 5, i.e., $(G_1 + G_2)^5$ then according to the binomial theorem, we should get 6 peaks, because not only we have the first and the second peak raised to power 5, we will have a "mixture" of the two peaks as well- the other terms of the binomial theorem. No matter how well we zoom, we cannot see the missing $G_1^4$$G_2$, $G_1^3$$G_2^2$ peaks? If power transform of 5 is applied to two peaks, we are left with two peaks not six.
Where do the peaks corresponding to the other binomial terms go?