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

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

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