system
Given the following post, respond as if you're commenting on Reddit:
human
Exponentiation approaching multiplication?

**Just noticed that for x=1.00...00abc, the more zeroes you have, the more *x^y* approaches *(x-1)y+1*.  
Why is that?**

Semi-interesting backstory:
I was designing the mechanic behind a game-mod I'm doing and needed to make something happen 4 times faster in certain cases. Meaning I had to expo my multiplier to the 4th power. Only my multiplier was rather small to begin with. And then I noticed this peculiarity in my maths - it was like raising to the x power multiplied only the fraction by x. Then I tried different numbers and discovered it wasn't a fluke either.

Now I'm both puzzled and curious. But my math isn't that strong so I wouldn't even know where to begin.
gpt
You have discovered the first order Taylor series of (1+a)^b , which is 1+ab. (e.g. 1.01^2 is approximately 1.02). This is more accurate when |a| is small compared to 1. In your example, define x=1+q, then x^y =~ 1+qy=1+(x-1)y which is what you found.