Мозок дуже важливий.

A natural pronunciation is:

мозо́к ду́же важли́вий

Roughly:

• мозо́к = mo-ZOK
• ду́же = DU-zhe
• важли́вий = vazh-LY-vyi

A few sound notes:

• ж sounds like the s in measure.
• в in Ukrainian is often softer than English v.
• и in важли́вий is not the same as English ee. It is a shorter, more central vowel.

It is in the nominative singular.

Why?

• It is the subject of the sentence.
• The sentence is basically Brain [is] very important.
• The dictionary form of the noun is also мозок.

So this is the basic subject form: мозок = brain.

Because важливий is an adjective agreeing with мозок.

Мозок is:

• masculine
• singular
• nominative

So the adjective also has to be:

• masculine
• singular
• nominative

That gives важливий.

Compare:

• мозок важливий = the brain is important
• книга важлива = the book is important
• питання важливе = the question is important

In Ukrainian, the present-tense copula to be is usually omitted in simple statements like this.

So:

• Мозок дуже важливий literally looks like Brain very important
• but it means The brain is very important

This is completely normal Ukrainian.

English needs is, but Ukrainian usually does not in the present tense.

Дуже means very.

It is an adverb, and here it modifies the adjective важливий:

• важливий = important
• дуже важливий = very important

Unlike adjectives, дуже does not change for gender, number, or case. It stays дуже.

The given order is the most neutral and natural:

• Мозок дуже важливий.

Ukrainian word order is more flexible than English, but changing it usually changes the emphasis, not the basic meaning.

For example:

• Мозок дуже важливий. = neutral
• Мозок важливий. = the brain is important
• Дуже важливий мозок. = possible, but this sounds marked and depends heavily on context

So for a learner, the safest version is the original one.

Yes. Ukrainian has no articles like a or the.

So мозок can mean:

• a brain
• the brain
• brain, depending on context

In this sentence, English would usually translate it as The brain is very important or sometimes just Brain is very important in a very general statement, though English normally prefers the brain.

Because in simple present-tense sentences with an omitted is, Ukrainian normally uses the adjective in the nominative:

• Мозок дуже важливий.

This is the standard everyday pattern.

English speakers sometimes expect something more complicated, but here it is straightforward:

• subject in nominative
• predicate adjective also in nominative form

You usually should not do that in ordinary speech.

The most natural everyday sentence is:

• Мозок дуже важливий.

Adding є in this kind of simple present-tense statement often sounds unnecessary or stylistically marked.

So as a learner, use the version without є unless you have a specific reason and know the style you want.

Yes. Важливий is the standard, neutral word for important.

So:

• дуже важливий = very important

That is the most useful word to learn for general situations:

• важливе питання = an important question
• важлива причина = an important reason
• важливий момент = an important moment

Yes, but not all in the same way.

• мозок is a noun, so it changes by case and number.
• важливий is an adjective, so it changes to agree with the noun.
• дуже does not change.

For example:

• важливий мозок = masculine singular
• важлива тема = feminine singular
• важливе питання = neuter singular
• важливі речі = plural

So in your sentence, важливий has the form it has because it matches мозок.