1. **State the problem:** Simplify the expression $2^{4x-1}$ and identify which of the given options it equals. 2. **Recall the properties of exponents:** - $a^{m+n} = a^m \times a^n$ - $a^{mn} = (a^m)^n$ - $a^{m-n} = \frac{a^m}{a^n}$ 3. **Rewrite the expression:** $$2^{4x-1} = \frac{2^{4x}}{2^1} = \frac{2^{4x}}{2}$$ 4. **Express $2^{4x}$ in terms of base 16:** Since $16 = 2^4$, then $$2^{4x} = (2^4)^x = 16^x$$ 5. **Substitute back:** $$2^{4x-1} = \frac{16^x}{2}$$ 6. **Conclusion:** The expression $2^{4x-1}$ simplifies to $\frac{16^x}{2}$. Therefore, the correct choice is **$16^x / 2$**.