1. The problem asks to find an expression equivalent to $$\frac{2^{-1}}{2^4}$$. 2. Recall the rule for dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. Apply this rule to the expression: $$\frac{2^{-1}}{2^4} = 2^{-1-4} = 2^{-5}$$. 4. Rewrite the negative exponent as a positive exponent in the denominator: $$2^{-5} = \frac{1}{2^5}$$. 5. Calculate $$2^5$$: $$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$$. 6. Therefore, the expression simplifies to: $$\frac{1}{32}$$. 7. The equivalent expression is $$\frac{1}{32}$$.