When dividing a fraction by another fraction, you multiply the one on top by the inverse of the one on the bottom.
[tex]\frac{\frac{1}{a^n}}{\frac{1}{a^n + 1} } = \frac{1}{a^n}*\frac{a^n+1}{1}\\[/tex]
so your answer should be
[tex]\frac{a^n +1}{a^n}[/tex]
Overall you were close, it just seems like you got the order mixed up.
