1. The problem is to express $ \frac{\frac{1}{2^4}}{\frac{1}{2^x}} $ as a simplified expression. 2. Recall the rule for dividing fractions: $ \frac{a/b}{c/d} = \frac{a}{b} \times \frac{d}{c} $. 3. Applying this rule, we get: $$ \frac{\frac{1}{2^4}}{\frac{1}{2^x}} = \frac{1}{2^4} \times \frac{2^x}{1} $$ 4. Multiply the numerators and denominators: $$ = \frac{1 \times 2^x}{2^4 \times 1} = \frac{2^x}{2^4} $$ 5. Use the exponent rule $ \frac{a^m}{a^n} = a^{m-n} $: $$ = 2^{x-4} $$ 6. Therefore, the simplified expression is $ 2^{x-4} $.