Punomoć i rukoznak su valjani.

Because they form a compound subject: punomoć i rukoznak = power of attorney and hand-sign/manual mark.

In Croatian, two singular nouns joined by i (and) normally take a plural verb:

• Punomoć je valjana. = The power of attorney is valid.
• Rukoznak je valjan. = The hand-sign is valid.
• Punomoć i rukoznak su valjani. = The power of attorney and the hand-sign are valid.

So su is the correct form of to be here.

The adjective has to agree with the subject in number and gender.

Here the subject is plural because it contains two items. But the two nouns have different genders:

• punomoć = feminine
• rukoznak = masculine

When Croatian has a mixed-gender plural subject, the normal default agreement is masculine plural. That is why you get:

• valjani

If both nouns were feminine, you would expect valjane.

• punomoć is feminine
• rukoznak is masculine

A useful way to see that is with demonstratives or singular adjectives:

• ta punomoć / punomoć je valjana
• taj rukoznak / rukoznak je valjan

A learner might find punomoć surprising because it ends in a consonant, but some feminine Croatian nouns do.

They are in the nominative singular.

They are the subject of the sentence, so nominative is expected. Each noun is singular by itself, but together they make a plural subject for agreement purposes.

Also, the predicate adjective after su is nominative plural:

• valjani

Here valjan means something like:

• valid
• legally acceptable
• in proper legal form

It is a very natural word in formal, legal, and administrative Croatian.

In many contexts, valjan is a bit more idiomatic and official-sounding than a direct international-looking alternative such as validan.

No, it is fairly formal and specialized.

A native speaker would be more likely to meet rukoznak in:

• legal texts
• administrative instructions
• official documents

So if this sentence feels formal, that is normal. The vocabulary is not especially conversational.

Yes. Croatian word order is fairly flexible.

The most neutral version is:

• Punomoć i rukoznak su valjani.

But you may also see:

• Punomoć i rukoznak valjani su.

That sounds more formal or stylistically marked. For learning purposes, the original order is the safest and most natural pattern to use.

Because Croatian does not have articles like English a/an and the.

So Croatian simply says:

• punomoć
• rukoznak

and the exact sense (a / the) is understood from context.

That means this sentence can be interpreted naturally in English as either:

• A power of attorney and a hand-sign are valid, or
• The power of attorney and the hand-sign are valid

depending on the situation.