### Instruction: Solve for $n$: $5^{2n + 1} = \frac{1}{25}$. Express your answer as a common fraction.### Response: So we have $5^{2n+1} = \frac{1}{25}$.
Right, let's first simplify the right side by rewriting the fraction as $5^{-2}$.
That's a good idea. Now we have $5^{2n+1} = 5^{-2}$.
And we can solve for $n$ by equating the exponents.
So we have $2n+1=-2$.