Is this how you prime factorize? and is that the correct answer?

You have the correct factor tree drawn out. Nice work on that. However, the final answer is not choice D.

The answer is actually choice C)

Notice how there are two '3's in the tree. One is below the 6 and the other is below the 126. So we really have 2*3*3*5*7 which turns into 2*3^2*5*7 which is what choice C is saying. 

Note: 2*3^2*5*7 is the same as  

Ithink the answer should be b.

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