What does a negative exponent mean in expressing Joules per cm?

I am a non-physicist so please take that into consideration here, but is:

$mJ/cm^{-2}$ the same thing as $J/cm^2$ ?

The negative exponent is a convention that I am seeing frequently in a type of calculation I am trying to make (calculating the dose of UVB light required to produce erythema or reddening on the skin), but I'm just not able to understand why a negative exponent is used in this way.

$Jcm^{-2}$ is equivalent to $J/cm^2$, as having $cm^{-2}$ is equivalent to saying $1/cm^2$ which in this case when multiplying by Joules gives us $J/cm^2$. However, it is not equivalent with $mJ$ in it, as that is a factor of $1000$ less than $J$ ($1000$ $mJ$ in a $J$).
• Also worth noting that OP compared $\frac {mJ}{cm^{-2}}$ and $\frac {J}{cm^2}$ which are actually different, as $\frac {mJ}{cm^{-2}}=m J \ cm^2$. I'm not sure if that was a typo or not. – JMac Aug 2 '17 at 19:13