How to interpret the formula on the earth, generally

[HairlessUncle]

Figure showing formula to calculate d, decrypt key.

Alright, while I studying RSA asymmetric encryption algorithm, there's common issue happen on myself again:
i can tell what each symbol means, but when they combined, i cant tell i really knew it ?.

Here's the actual question:
which does that -1 means, inverse or ^ -1
if it was ^ -1, then isn't it could be written as d = 1 (mod ∅ (n))/ e ????

(attached figure are the full steps)

 

[blamocur]

Yes, [imath]e^{-1}[/imath] here means [imath]\frac{1}{e}[/imath] in modular arithmetic. And no, you cannot rewrite it as [imath]\frac{1 \mod\phi(n)}{e}[/imath]. You might want to check Wikipedia or other sources on modular arithmetic.