1. **State the problem:** Simplify the expression $$\frac{2^{n-1}}{3^n}$$. 2. **Recall the properties of exponents:** - When dividing powers with the same base, subtract the exponents. - When raising a power to another power, multiply the exponents. 3. **Rewrite the numerator:** $$2^{n-1} = 2^n \times 2^{-1} = \frac{2^n}{2}$$ 4. **Substitute back into the expression:** $$\frac{2^{n-1}}{3^n} = \frac{\frac{2^n}{2}}{3^n} = \frac{2^n}{2 \times 3^n}$$ 5. **Write the denominator as a product:** $$2 \times 3^n = 2 \times 3^n$$ 6. **Final simplified form:** $$\frac{2^n}{2 \times 3^n} = \frac{2^n}{2 \cdot 3^n}$$ This is the simplest form unless you want to write it as: $$\frac{2^n}{2 \cdot 3^n} = \frac{1}{2} \times \left(\frac{2}{3}\right)^n$$ **Answer:** $$\boxed{\frac{1}{2} \left(\frac{2}{3}\right)^n}$$