Learn Russian: По рассмотрении вашей заявки мы немедленно примем решение. - Upon consideration of your application, we will immediately make a decision.

The preposition по usually takes the Dative case. However, in formal Russian, when по is used to mean "upon" or "immediately after" an event, it requires the Prepositional case. That is why we use the Prepositional form по рассмотрении (upon consideration).

Why does the Prepositional case form рассмотрении end in -ии instead of the usual -е?

The dictionary form is рассмотрение, which is a neuter noun ending in -ие. As a rule, nouns that end in -ия, -ий, and -ие always take -ии in the Prepositional case rather than the standard -е ending.

Why is вашей заявки in the Genitive case here?

It translates to "of your application". When one noun modifies another directly like this (the consideration of your application), the second noun goes into the Genitive case to show that relationship.

Why do we use the verb примем to mean "make" a decision?