Proszek był na podłodze, więc wzięłam ścierkę i wiadro.

Because the sentence is in the past tense.

• był = was
• It is the past tense of być = to be
• It agrees with proszek, which is a masculine singular noun

So:

• proszek jest na podłodze = the powder is on the floor
• proszek był na podłodze = the powder was on the floor

Because the speaker is female.

In Polish, the past tense changes depending on the gender of the speaker in the 1st person singular:

• wzięłam = I took (said by a woman)
• wziąłem = I took (said by a man)

That is very normal in Polish and happens with many past-tense verbs:

• zrobiłam / zrobiłem = I did
• poszłam / poszedłem = I went

The dictionary form is wziąć, meaning to take.

wzięłam is a past-tense form built from that verb.

A learner often finds this difficult because the forms look quite different:

• infinitive: wziąć
• past tense, feminine singular: wzięłam
• past tense, masculine singular: wziąłem

This is just one of those verbs whose forms need to be learned as a pattern.

Because wziąć is the perfective verb, and here it fits the idea of a completed action: she took the cloth and bucket.

Polish often has verb pairs:

• brać = to be taking / to take in an ongoing or repeated sense
• wziąć = to take once, successfully, completely

In this sentence, the action is a single finished event, so wzięłam is the natural choice.

Because this sentence describes location, not movement.

With na, Polish can take different cases:

• na + locative = on, at a place
• na + accusative = onto, toward a surface/destination

Here the powder was on the floor, so we use locative:

• na podłodze = on the floor

Compare:

• Proszek był na podłodze = The powder was on the floor
• Wysypałam proszek na podłogę = I spilled the powder onto the floor

Because after na in the meaning of location, the noun goes into the locative case.

The noun is:

• podłoga = floor

Its locative singular is:

• podłodze

So:

• na podłodze = on the floor

This change is just normal Polish case inflection.

Because ścierkę is the accusative singular form, and it is the direct object of wzięłam.

The basic form is:

• ścierka = cloth / rag / dishcloth

But after a verb like wziąć when it is the thing taken, we use the accusative:

• wzięłam ścierkę = I took a cloth

For many feminine nouns ending in -a, the accusative singular ends in -ę:

• książka → książkę
• herbata → herbatę
• ścierka → ścierkę

Because wiadro is a neuter noun, and in the singular its accusative form is the same as its nominative form.

So:

• wiadro = bucket
• wzięłam wiadro = I took a bucket

This is different from many feminine nouns, which often change form in the accusative.

So in the sentence:

• ścierkę changes
• wiadro stays the same

Because Polish often omits subject pronouns when they are not needed.

The verb form itself already tells you the subject:

• wzięłam clearly means I took and also shows the speaker is female

So ja is unnecessary unless you want emphasis or contrast.

Compare:

• Wzięłam ścierkę i wiadro = I took a cloth and a bucket
• Ja wzięłam ścierkę i wiadro = I took a cloth and a bucket (with extra emphasis on I)

więc means so, therefore, or thus.

It links the first part of the sentence to the result:

• Proszek był na podłodze = The powder was on the floor
• więc wzięłam ścierkę i wiadro = so I took a cloth and a bucket

It is a very common word for showing consequence.

Because in Polish, więc often introduces a new clause expressing a result, and it is normally separated by a comma.

So the punctuation here is standard:

• Proszek był na podłodze, więc wzięłam ścierkę i wiadro.

This is similar to English, where a comma is often used before so when it links two full clauses.

Because Polish usually does not need a dummy subject like English there.

English often says:

• There was powder on the floor

Polish simply says:

• Proszek był na podłodze

Literally this is more like:

• Powder was on the floor

That is a normal Polish way to express existence or presence.

Yes. Polish word order is more flexible than English, although the original sentence sounds natural and neutral.

The sentence:

• Proszek był na podłodze, więc wzięłam ścierkę i wiadro.

is a straightforward, natural order.

You could sometimes change the order for emphasis, for example:

• Na podłodze był proszek, więc wzięłam ścierkę i wiadro.

This puts more focus on where the powder was.

So the meaning stays similar, but the emphasis can change.

Proszek most basically means powder, but in real life it can refer to different kinds of powder depending on context.

For example, it can mean:

• powder in general
• washing powder / detergent
• some other powdered substance

In this sentence, because it is on the floor and someone takes a cloth and bucket, the exact kind of powder is understood from the situation rather than from the word alone.

Usually yes. Ścierka often means a cloth, dishcloth, or rag, depending on context.

In this sentence, because the speaker is about to clean up powder from the floor, ścierka is best understood as a cleaning cloth / rag.

So the word is broad, but the situation makes the intended meaning clear.