(S) \( 2^{3} \cdot 2^{-5} \cdot 3^{-3} \cdot 3^{2} \)

To simplify \( 2^{3} \cdot 2^{-5} \cdot 3^{-3} \cdot 3^{2} \), you can use the laws of exponents. Start by combining the powers of the same base. For the base \( 2 \): \[ 2^{3} \cdot 2^{-5} = 2^{3 + (-5)} = 2^{-2} \] And for the base \( 3 \): \[ 3^{-3} \cdot 3^{2} = 3^{-3 + 2} = 3^{-1} \] Now, putting it all together: \[ 2^{-2} \cdot 3^{-1} = \frac{1}{2^{2}} \cdot \frac{1}{3^{1}} = \frac{1}{4} \cdot \frac{1}{3} = \frac{1}{12} \] Therefore, the simplified expression is: \[ \frac{1}{12} \]