Learn Russian: В кабинете большое кресло.

Even though you are practicing the prepositional case, большое кресло (the big armchair) is the subject of this sentence—it is the thing that is in the study. The subject of a sentence always stays in the nominative (dictionary) case. Only the location (в кабинете) uses the prepositional case here.

Where are the words for "there is" in the Russian sentence?

Russian typically drops the verb "to be" (is, am, are) in the present tense, and it doesn't use a filler word like "there" to talk about existence. You simply state the location and the item: В кабинете большое кресло literally translates to "In the study [is a] big armchair."

Why does кабинете end in -е?

The dictionary form is кабинет (study or office), which is a masculine noun ending in a consonant. To say in the study, we use the preposition в (in) and put the noun in the prepositional case to show location. For most masculine nouns, you do this by adding -е.

Why does the adjective большое end in -ое?

Adjectives must match the noun they describe in gender, number, and case. кресло (armchair) is a neuter noun (because it ends in -о). Therefore, the dictionary form of the adjective большой (big) changes its ending to the neuter nominative form, which is -ое.