1. **Problem statement:** A cube has a volume of 216 cm³. We need to find: a) A power expression for the edge length of the cube. b) A power expression for the surface area of the cube. c) The exact edge length and surface area. 2. **Formulas and rules:** - Volume of a cube: $$V = s^3$$ where $s$ is the edge length. - Surface area of a cube: $$A = 6s^2$$ 3. **Part a) Edge length power expression:** Since $$V = s^3$$, the edge length is $$s = \sqrt[3]{V} = V^{\frac{1}{3}}$$. So the power expression for edge length is $$s = 216^{\frac{1}{3}}$$. 4. **Part b) Surface area power expression:** Surface area is $$A = 6s^2$$. Using the power expression for $s$, we get: $$A = 6 \left(216^{\frac{1}{3}}\right)^2 = 6 \times 216^{\frac{2}{3}}$$. 5. **Part c) Calculate exact values:** Calculate edge length: $$s = 216^{\frac{1}{3}}$$ Since $$216 = 6^3$$, then: $$s = (6^3)^{\frac{1}{3}} = 6^{3 \times \frac{1}{3}} = 6^1 = 6$$ cm. Calculate surface area: $$A = 6s^2 = 6 \times 6^2 = 6 \times 36 = 216$$ cm². **Final answers:** - Edge length: $6$ cm - Surface area: $216$ cm²