1. **State the problem:** Find the exact volume of a cylinder with radius $r=4$ inches and height $h=8$ inches. 2. **Formula:** The volume $V$ of a cylinder is given by the formula: $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Substitute the values:** $$V = \pi \times 4^2 \times 8$$ 4. **Calculate the square of the radius:** $$4^2 = 16$$ 5. **Multiply:** $$V = \pi \times 16 \times 8$$ 6. **Simplify multiplication:** $$V = \pi \times 128$$ 7. **Final exact volume:** $$V = 128\pi \text{ in}^3$$ This is the exact volume of the cylinder in cubic inches.