Solve each equation. \( 25^{-x}=625 \)

To solve the equation \( 25^{-x} = 625 \), we can start by expressing both sides as powers of \( 5 \). We know that \( 25 = 5^2 \) and \( 625 = 5^4 \). This allows us to rewrite the equation as: \[ (5^2)^{-x} = 5^4 \] Simplifying the left side gives us: \[ 5^{-2x} = 5^4 \] Since the bases are the same, we can set the exponents equal to each other: \[ -2x = 4 \] Now, solving for \( x \) involves dividing both sides by -2: \[ x = \frac{4}{-2} = -2 \] So, the solution to the equation \( 25^{-x} = 625 \) is \( x = -2 \).