How to simplify the product of two $\exp$ functions It's been a while since I did any of this.  I have the following product: $\exp(-j2 \pi u|k|x) \cdot \exp(-j2 \pi v |k|x)$.  This seems like it is something that can be simplified, but how?  Note, that is not convolution, it is simple multiplication.  Thanks!

$$\exp(-j2 \pi u|k|x) \cdot \exp(-j2 \pi v |k|x)=\exp\big(-j2\pi u|k|x-j2\pi v|k|x\big) $$
$$=\exp(-j2\pi (u+v)|k|x).$$
Exponentials obey $a^ba^c=a^{b+c}$ (though there can be branching issues for complex $a$).
