The standard form of an exponential function looks something like this:
$$ a(b)^{cx-h}+k $$
- $a$: Vertical stretch/compression
- $c$ Horizontal stretch/compression
- $h$: Horizontal translation left or right
- $k$: Vertical translation up or down

Without stretch:
$$ a^{x-b}+c $$

A negative exponent is the equivalent of `1/x`, EG
$$ x^{-2} = \frac{1}{x^2} $$
An equation in the base form $2^x$ will have an asymptote of $y = 0$. 

Putting a negative in front of something like $2^x$ flips it over the *x axis* ($-2^x$).
Putting a negative in front of the exponent ($2^{-x}$) flips it over the y axis.