1. **State the problem:** Simplify the expression $$\left(\frac{2^3}{2^2} \cdot 2^2\right)^4$$. 2. **Recall the exponent rules:** - When dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$. - When multiplying powers with the same base: $$a^m \cdot a^n = a^{m+n}$$. - When raising a power to another power: $$(a^m)^n = a^{m \cdot n}$$. 3. **Simplify inside the parentheses:** $$\frac{2^3}{2^2} \cdot 2^2 = 2^{3-2} \cdot 2^2 = 2^1 \cdot 2^2$$ 4. **Multiply powers inside the parentheses:** $$2^1 \cdot 2^2 = 2^{1+2} = 2^3$$ 5. **Raise the result to the 4th power:** $$\left(2^3\right)^4 = 2^{3 \cdot 4} = 2^{12}$$ 6. **Final answer:** $$2^{12}$$