1. **State the problem:** Solve the equation $2^{2x-1} = \frac{1}{16}$ for $x$. 2. **Recall the formula and rules:** We know that $16 = 2^4$, so $\frac{1}{16} = 2^{-4}$ because $\frac{1}{a^n} = a^{-n}$. 3. **Rewrite the equation using the same base:** $$2^{2x-1} = 2^{-4}$$ 4. **Set the exponents equal:** Since the bases are the same and nonzero, the exponents must be equal: $$2x - 1 = -4$$ 5. **Solve for $x$:** $$2x - 1 = -4$$ Add 1 to both sides: $$2x - \cancel{1} + \cancel{1} = -4 + 1$$ $$2x = -3$$ Divide both sides by 2: $$x = \frac{-3}{2}$$ **Final answer:** $$x = -\frac{3}{2}$$