How is the word "Subhan Allah wa bihamdihi" and the phrase "Allahumma la aisha illa aish al-akhirah" formed?

The word "Allah" in "Subhan Allah" (Glory be to Allah) has a kasra (vowel mark for 'i') on the "ha" because it is in the genitive case (mudhaf ilayh).

In "La 'aisha illa 'aish al-akhirah" (There is no life but the life of the Hereafter): The first "'aish" is in the accusative case (mansub) with a fat-ha, the second "'aish" is in the nominative case (marfu') with a dhamma, and "al-akhirah" is in the genitive case (majrurah) with a kasra.