Use the relevant properties of exponents to simplify the following expression. Answer should only have positive exponents. \[ \left(\frac{3^{-3}}{3^{5}}\right)^{4} \]

To simplify the expression \(\left(\frac{3^{-3}}{3^{5}}\right)^{4}\), first, apply the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\). This gives us: \[ \frac{3^{-3}}{3^{5}} = 3^{-3-5} = 3^{-8}. \] Now we raise \(3^{-8}\) to the power of 4: \[ (3^{-8})^{4} = 3^{-8 \cdot 4} = 3^{-32}. \] To write this with positive exponents, we use the property \(a^{-m} = \frac{1}{a^{m}}\): \[ 3^{-32} = \frac{1}{3^{32}}. \] Thus, the simplified expression is: \[ \frac{1}{3^{32}}. \]