1. **State the problem:** Simplify the expression $\frac{2^3 \times 2^2}{2^4}$. 2. **Recall the exponent rules:** When multiplying powers with the same base, add the exponents: $a^m \times a^n = a^{m+n}$. When dividing powers with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$. 3. **Apply multiplication rule:** $$2^3 \times 2^2 = 2^{3+2} = 2^5$$ 4. **Apply division rule:** $$\frac{2^5}{2^4} = 2^{5-4} = 2^1$$ 5. **Simplify the final expression:** $$2^1 = 2$$ **Final answer:** $2$