# How do I prove that, if $a$ divides $b$, then $a^n$ divides $b^n$? [duplicate]

This question already has an answer here:

How would I prove the following?

If $$a$$ divides $$b$$, then $$a^n$$ divides $$b^n$$.

## marked as duplicate by Key Flex, Don Thousand, max_zorn, Shailesh, LeucippusOct 31 '18 at 4:05

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• what have you tried? – Siong Thye Goh Oct 31 '18 at 2:39
• We aren't here to do your homework. You need to display some effort. – Aaron Zolotor Oct 31 '18 at 2:45
• @KeyFlex: The question you link to is the (more interesting) converse of this question, so it is not a duplicate. – JavaMan Oct 31 '18 at 2:48

## 1 Answer

$$a \mid b \to b = a c$$ so $$b^n = a^n c^n \to a^n \mid b^n$$.

• My goodness. I'd love an explanation why my answer is wrong or inappropriate. – David G. Stork Oct 31 '18 at 2:41
• Just gave ya an upvote. Maybe more detail would be good (though there isn't too much to add really) but I don't see an issue – Aaron Zolotor Oct 31 '18 at 2:45
• Some might downvote this answer not because it is wrong, but because you are doing OP's homework for them with no hints and therefore no chance for them to learn from your answer. As a side note, you can use the Latex command a \mid b to produce $a \mid b$ – JavaMan Oct 31 '18 at 2:51