What is meant by the notation $A^{\times{B}}_{\div{C}}$; where A,B,C are real numbers? I have come across a few papers using the notation $A^{\times{B}}_{\div{C}}$; where A,B,C are real number. For example, $3000^{\times{3}}_{\div{4}}$.
An example can be Eqn (4) in Stern &amp; Laor (2012) &quot;Type 1 AGN at low $z$ – II. The relative strength of narrow lines and the nature of intermediate type AGN&quot;, which reads as follows:

$$\frac{L_{\rm bol}}{10^{43}\ \rm erg\ s^{-1}} = 4000^{\times 4}_{\div 4} \left( \frac{L_{\rm [O\ III]}}{10^{43}\ \rm erg\ s^{-1}}\right)^{1.39}$$

What is the generic meaning of this notation?
A confirmation of the explanation is given slightly further on where it talks about how the uncertainty is derived:

In equation (4) we use the 0.6 dex scatter of $\log L_{\rm UV}$ around
the $L_{\rm UV}$ versus $L_{\rm [O\ III]}$ relation, as an estimate for the uncertainty
in deriving $L_{\rm bol}$ from $L_{\rm [O\ III]}$.

The term &quot;dex&quot; indicates a base-10 logarithm of a unit, which translates into a factor of $10^{0.6} \approx 4$. So translating the error expressed in the logarithm of the quantity into an error expressed on the quantity itself, this becomes &quot;multiply-or-divide by 4&quot;, which here is rendered $4000^{\times 4}_{\div 4}$.
Pela's excellent answer explicitly goes into detail about what this implies for the probability distribution. I usually prefer notation like $10^{x \pm \sigma}$ which sticks to more familiar notation and explicitly implies something vaguely log-normal rather than normal, although perhaps it gets a bit cramped when asymmetric error bars come into play.