Prudentia sine sapientia non multum valet, sed utraque discipulae utilis est.

Because these are first-declension nouns, and in the singular:

• the nominative ends in -a
• the ablative ends in -ā

In texts without macrons, both are usually written the same way. So:

• prudentia = nominative singular, the subject
• sapientiā = ablative singular after sine

The preposition tells you the case of sapientia, even if the spelling looks identical.

Because sine always takes the ablative case. So:

• sine sapientiā = without wisdom

That is a fixed Latin construction. After sine, you should expect an ablative.

The verb valet comes from valeo, which can mean things like:

• be strong
• be effective
• be worth something
• have force

Here, with multum, it means something like:

• is not worth much
• does not count for much
• does not have much value

So the idea is not physical strength, but rather importance or usefulness.

Because multum here is being used adverbially, meaning much.

So:

• non multum valet = it is not worth much

It is not modifying a noun, so it is not the adjective multa. Latin often uses the neuter singular form this way as an adverb.

They overlap, but they are not exactly the same.

• prudentia often suggests practical judgment, discretion, or good sense in action
• sapientia often suggests wisdom in a broader or deeper sense

So the sentence contrasts practical good judgment with deeper wisdom: prudence by itself is limited if it is not guided by wisdom.

utraque is the feminine form of uterque, meaning:

• each of the two
• often naturally translated as both

Here it refers back to the two feminine nouns:

• prudentia
• sapientia

So utraque means each of the two qualities or, in smoother English, both.

Because Latin uterque / utraque / utrumque is grammatically singular, even though it refers to two items.

Its basic sense is each one of the two. English often uses both instead, but Latin still treats the word as singular.

That is why the sentence has:

• utraque
• utilis
• est

all in the singular.

For the same reason: utraque is grammatically singular.

Even though it refers to two things, Latin is thinking in terms of each of the two rather than a normal plural. So:

• utraque ... est = each of the two is ...

English may prefer both are, but Latin uses the singular here.

Not in the way you should analyze this sentence.

Here utraque is a complete form of the pronoun uterque. You should learn it as one word meaning each of the two / both.

So do not read it as:

• utra
  • and

In this sentence, -que is just part of the word utraque.

Because discipulae is dative singular here, and the adjective utilis commonly takes a dative:

• alicui utilis = useful to someone

So:

• discipulae utilis est = is useful to the student

English uses to or for; Latin often uses the dative case instead.

The form discipulae could, in isolation, be several things:

• genitive singular
• dative singular
• nominative plural

But in this sentence, the construction makes the choice clear:

• utilis regularly goes with the dative of the person affected or benefited

So discipulae must mean to the student, not of the student or the students.

Because the dative case ending already expresses that idea.

Latin often uses case endings where English uses prepositions. So instead of saying:

• useful to the student

Latin can simply say:

• discipulae utilis

with the dative ending doing the work of English to/for.

Latin word order is much more flexible than English word order.

This sentence is arranged in a natural and elegant way:

• Prudentia comes first as the topic
• sine sapientia immediately qualifies it
• sed introduces the contrast
• utraque begins the second clause clearly
• discipulae utilis est puts the person benefited near utilis

A different order could still be grammatical, but this order gives a clear contrast and smooth emphasis.