Mat 17:26 Then are the children free.

KJV Verse: 

Mat 17:26 Then are the children free.

Literal Alternative: 

For this reason, the children are free [people]. 

Hidden Meaning: 

This is a much more interesting statement than its seems on the surface: a punch line. After Peter says that his master, Christ pays tribute, Christ asks if the children of the king of the earth are required to pay taxes. Peter says that they are not. This leads Christ to observe here that the children of king's are free.

"Children" is from the Greek word that means a "son," and more generally, a "child." To understand this verse, we must imagine Christ indicating himself as he said "sons." Christ frequently refers to himself as "the son of man," and occasionally, though usually less directly, as "the son of God." More in this article about "son of" statements

The verb here is the common form of "to be" in Greek. It means to have a certain characteristic or remain in a certain condition. 

"Free" is from an adjective which means "free," "freedom," "independent," and "freed from a thing." Christ uses it rarely. 

This answer implies a number of things.

First, it implies taxation is a form of slavery. In Christ's era, this was more obvious because slavery was understood as the order of things. Everyone knew that there were masters and servants. Those that denied that the state was their master were dealt with harshly.

Second, though children are subservient to the parents, their role is not one of slaves. They were "free" because there had a lifetime stake in the house. Something Christ states explicitly in Jhn 8:35 and Jhn 8:36.

Finally, by challenging the idea that he should pay tribute, he is claiming to be a child of the ruler of the planet. This is a play on words and why he did not refer to the "world," that is, human society, in the previous verse, but to the "rulers of the planet." As the son of God, Christ is suggesting he is a son of the ruler and therefore, should be free of taxes. 

We should also remember that Christ refers to all of us as sons of God. So this is a statement that we should all be free.  This is why the idea of America could only come out of Christianity. Those who put their faith in governments still see the world as masters controlling slaves, not a world of free people under God.  

Wordplay: 

Christ is subtly referring to himself as the son of the ruler. 

Vocabulary: 

Ἄραγε "Then" is from ara, which means "there and then," "straightway," "then," "next," "mark you!," "for this cause," "so true is it that," and "namely." 

ἐλεύθεροί (noun pl masc nom)"Free" is from eleutheros, which means "free," "freedom," "independent," "unencumbered (of property)," "fit for a freeman," "frank," "legally permissible," "open to," of things: "free," "open to all,"and "freed from a thing."

εἰσιν (verb 3rd pl pres ind act) "Is" is from eimi, which means "to be," "to exist," "to be the case," and "is possible." 

οἱ υἱοί: (noun pl masc nom) "The chidren" is from huios, which means a "son," and more generally, a "child." -- The word translated as "son" more generally means "child."