Why does soda explode if artificial sweetener or other powders are added?
Artificial sweetener powder causes nucleation of the carbonation in the soda/pop/soda-pop. The carbon dioxide concentration in the soda is higher than the equilibrium concentration for the partial pressure of $\ce{CO2}$ in the atmosphere thus over time the soda will off-gas $\ce{CO2}$ and if allowed to sit long enough will become "flat".

The off-gassing is spontaneous but not instantaneous, thus it is subject to kinetic rates. To form a bubble, enough $\ce{CO2}$ molecules need to coalesce at one time to form a large enough bubble to be stable and not redissolved in the soda (nucleating). 

When a rough surface is introduced, the number of $\ce{CO2}$ molecules that must come together to form a stable bubble is far less that the pure drink, so the off-gassing occurs much faster causing the observed "explosion".

You can observe this when certain glasses (ussually beer glasses) etch a small ring in the glass, creating a rough surface and the formation of bubbles at the ring.  you can also observe this if you put a larger rough object in the soda. This could be a rock, a piece of wood (like a tooth pick), or even a Mentos.

To solve this you might be able to dissolve it in a small amount of water first. This may not completely solve issue though, as most sweeteners use silicon oxide or titanium oxide powder to prevent clumping, neither of which are soluble and will still nucleate bubbles.