### Instruction: Solve for $n$: $5^{2n + 1} = \frac{1}{25}$. Express your answer as a common fraction.### Response: To solve for $n$, I need to get rid of the exponent on the left-hand side.
I notice that 25 is a power of 5, namely $25 = 5^2$.
I can rewrite the equation using this fact: $5^{2n + 1} = 5^{-2}$.
Now I have the same base on both sides, so I can equate the exponents: $2n + 1 = -2$.