Write as a single power of 3 : \[ \frac{\left(3^{2}\right)^{-2}}{3^{5} \times 3^{-1}} \]

To express the given expression as a single power of 3, we can first simplify the expression step by step. Starting with: \[ \frac{\left(3^{2}\right)^{-2}}{3^{5} \times 3^{-1}} \] First, simplify the numerator \(\left(3^{2}\right)^{-2}\): \[ \left(3^{2}\right)^{-2} = 3^{2 \cdot (-2)} = 3^{-4} \] Now, simplify the denominator \(3^{5} \times 3^{-1}\): \[ 3^{5} \times 3^{-1} = 3^{5 + (-1)} = 3^{4} \] Now we can rewrite the expression: \[ \frac{3^{-4}}{3^{4}} \] When dividing exponents with the same base, we subtract the exponents: \[ 3^{-4 - 4} = 3^{-8} \] Thus, the expression as a single power of 3 is: \[ \boxed{3^{-8}} \]