Dux femina prudens milites ad urbem ducit.

Yes. They refer to the same person and are both in the nominative singular.

This is a very common Latin construction called apposition: one noun is followed by another noun that renames or identifies it more specifically.

So dux femina means something like:

• the leader, a woman
• the leader, who is a woman
• or more smoothly in English, the female leader

Latin often does this without any extra word like who is.

Latin can certainly use adjectives meaning female, but here it uses the noun femina to identify the leader as a woman.

Using a noun in apposition can feel more concrete or emphatic: not just female, but a woman.

So dux femina is not literally adjective + noun. It is noun + noun:

• dux = leader
• femina = woman

Both point to the same person.

Because prudens is a third-declension adjective with the same nominative singular form for masculine and feminine.

So:

• masculine: prudens
• feminine: prudens
• neuter: prudens

That means the form does not change just because it describes a woman.

This is different from first/second-declension adjectives such as bonus, bona, bonum, where the feminine form does look different.

Grammatically, it is easiest to take prudens with femina, since they stand next to each other:

• femina prudens = a wise woman

But because femina is in apposition to dux, the adjective ultimately describes the same person who is the leader.

So in practice, prudens tells us that the leader is wise.

Because milites could be either nominative plural or accusative plural in form, but the verb helps you decide.

• ducit = he/she leads, singular
• milites = soldiers, plural

Since the verb is singular, milites cannot be the subject here. The singular subject is dux femina prudens, and milites must be the direct object.

So the structure is:

• subject: dux femina prudens
• object: milites
• verb: ducit

Because ad normally takes the accusative case when it means motion to or toward a place.

So:

• urbs = nominative, city
• urbem = accusative, city as the object of motion toward

Thus:

• ad urbem = to the city / toward the city

This is a very common Latin pattern:

• ad villam = to the house/farm
• ad portam = to the gate
• ad urbem = to the city

It shows direction or destination. It tells you where the soldiers are being led.

So ducit milites ad urbem means:

• leads the soldiers toward the city
• leads the soldiers to the city

It is a prepositional phrase modifying the verb ducit.

Because Latin word order is much freer than English word order.

Latin often places the verb at or near the end of the sentence, especially in straightforward prose. That means a Latin sentence may look more like:

• subject
• object
• other details
• verb

So Dux femina prudens milites ad urbem ducit is a very natural Latin order.

English usually prefers The wise female leader leads the soldiers to the city, with the verb earlier.

Often, yes. Because Latin uses case endings, the roles of the words are shown mainly by their forms, not by position.

For example, these would still express basically the same idea:

• Milites dux femina prudens ad urbem ducit.
• Ad urbem dux femina prudens milites ducit.
• Dux milites ad urbem ducit.

However, different word orders can change emphasis. Putting a word earlier or later may draw attention to it.

Because Latin has no articles like English the and a/an.

So a noun like dux can mean:

• a leader
• the leader

The context tells you which is best in English.

The same is true for milites and urbem:

• soldiers / the soldiers
• a city / the city

When translating into English, you add the article that sounds natural from the context.

Ducit is:

• present tense
• third person singular
• active voice
• from the verb ducere = to lead

So it means:

• he leads
• she leads
• it leads

Here it must mean she leads, because the subject is a woman.

Because Latin verbs do not change form for masculine vs. feminine subjects in the present tense.

So ducit can mean:

• he leads
• she leads
• it leads

The subject tells you which one is intended.

That is why dux femina prudens is important: it tells you the subject is female, so in English you translate ducit as she leads.

Dux is a noun of common gender. That means the same form can refer to either a male or a female leader.

So:

• a male leader can be dux
• a female leader can also be dux

The sentence makes the leader female by adding femina.

This is something English speakers often notice, because the noun itself does not change shape to show gender. Latin often relies on context or additional words for that.

Yes, that is a reasonable smooth English rendering, even though the Latin structure is not exactly the same as an English adjective chain.

More literally, the Latin is closer to:

• the leader, a wise woman, leads the soldiers to the city

But English often prefers a more compact expression such as:

• the wise woman leader
• the wise female leader

So the smoother English phrase is fine, as long as you understand the Latin grammar underneath it.