La modemo estas apud la enkursigilo.

Because la is the Esperanto definite article, meaning the. It is used separately with each definite noun phrase:

• la modemo = the modem
• la enkursigilo = the router

So Esperanto does not use one la to cover both nouns here. Each noun phrase gets its own article.

Also, Esperanto has only one article, la. It does not change for gender, number, or case.

No. Esperanto has no indefinite article.

So:

• modemo can mean a modem or just modem
• la modemo means the modem

That is why la is important here: it tells you the speaker means a specific modem and a specific router.

Estas is the present-tense form of esti, meaning to be.

A very learner-friendly feature of Esperanto is that the verb does not change depending on the subject:

• mi estas = I am
• vi estas = you are
• li estas = he is
• ŝi estas = she is
• ĝi estas = it is
• ili estas = they are

So in this sentence, La modemo estas... simply means The modem is...

Apud is a preposition meaning next to, beside, or by.

In this sentence, it shows location: the modem is positioned beside the router.

It usually suggests fairly close physical proximity. In some contexts, English near might be translated with other words, but apud is a very natural choice for beside / next to.

Because there is no direct object here, and the location phrase uses a preposition.

A few key points:

• La modemo is the subject.
• estas links the subject to information about its location.
• apud la enkursigilo is a prepositional phrase.

Normally, nouns after prepositions do not take -n:

• apud la enkursigilo = beside the router

The -n ending is mainly used for direct objects and sometimes for direction/motion in certain expressions. This sentence describes location, not movement, so no -n is needed.

Because -o is the standard noun ending in Esperanto.

So:

• modem-o = modem
• enkursigil-o = router

This is one of the most regular parts of Esperanto grammar: if a word ends in -o, it is a noun.

If you made them plural, they would become:

• modemoj = modems
• enkursigiloj = routers

Yes. Esperanto words are often built from smaller meaningful pieces.

enkursigilo can be analyzed like this:

• en- = in, into
• kurs = course, route
• -ig- = make/ cause
• -il- = tool, instrument
• -o = noun

So enkursigilo is roughly a tool/device that causes routing into a path. In practice, it simply means router.

Even if the full breakdown feels a bit abstract at first, it is useful because Esperanto often forms technical vocabulary this way. Over time, these parts become very helpful.

This order is the most straightforward and neutral:

• La modemo estas apud la enkursigilo.

But Esperanto word order is fairly flexible, especially because grammar endings make the roles of words clearer.

For example, you could also say:

• Apud la enkursigilo estas la modemo.

That still means essentially the same thing, but it puts more focus on the location first, a bit like Next to the router is the modem.

So the original order is the most natural for a basic statement, but it is not the only possible order.

Esperanto pronunciation is very regular. A rough guide is:

• La = lah
• modemo = mo-DE-mo
• estas = ES-tas
• apud = a-PUD
• la = lah
• enkursigilo = en-kur-si-GI-lo

The stress in Esperanto is almost always on the second-to-last syllable, which is why you get:

• moDEmo
• EStas
• aPUD
• en-kur-siGIlo

Because this sentence contains only nouns, a verb, an article, and a prepositional phrase. There is no adjective in it.

The parts are:

• la = article
• modemo = noun
• estas = verb
• apud = preposition
• la = article
• enkursigilo = noun

If you wanted to add an adjective, you would use -a, for example:

• La nova modemo estas apud la malnova enkursigilo.
• The new modem is next to the old router.

Sometimes, yes, but the meaning would change slightly.

For example:

• ĉe often means at, with, or by
• proksime al means near to
• apud means beside / next to

So if you want the idea of one object being right by another, apud is a very good choice.

If you used ĉe la enkursigilo, it might sound a bit less specifically next to and more generally at the router / by the router, depending on context.