Simplify the expression. Write the result using positive exponents. \( \frac{2^{-3} x^{-5}}{2^{3} x} \)

To simplify the expression \( \frac{2^{-3} x^{-5}}{2^{3} x} \), we apply the rules of exponents. Starting with the \(2\) terms, we have: \[ \frac{2^{-3}}{2^{3}} = 2^{-3-3} = 2^{-6} \] Now, for the \(x\) terms: \[ \frac{x^{-5}}{x} = x^{-5-1} = x^{-6} \] Combining these results gives us: \[ 2^{-6} x^{-6} = \frac{1}{2^{6} x^{6}} \] This results in the final simplified expression: \[ \frac{1}{64x^{6}} \] Thus, the simplified expression using positive exponents is \( \frac{1}{64x^{6}} \).