Use the like bases property to solve the equation \( 625^{n}=\frac{1}{25} \) \( n=\square \)

To solve the equation \( 625^{n}=\frac{1}{25} \), we first rewrite both sides with a common base. We know that \( 625 = 25^2 \) and \( \frac{1}{25} = 25^{-1} \). Substituting these values in gives us: \[ (25^2)^{n} = 25^{-1} \] Using the power of a power property, we can simplify the left side: \[ 25^{2n} = 25^{-1} \] Now that we have like bases, we can set the exponents equal to each other: \[ 2n = -1 \] Solving for \( n \) gives us: \[ n = \frac{-1}{2} \] So, the solution is: \( n = -\frac{1}{2} \)