1. **Problem:** A rectangular prism has a volume of 80 cubic inches. 2. **Formula:** Volume of a rectangular prism is given by $$V = l \times w \times h$$ where $l$ is length, $w$ is width, and $h$ is height. 3. **Part a:** If length, width, and height are all doubled, the new volume is: $$V_{new} = (2l) \times (2w) \times (2h) = 2 \times 2 \times 2 \times lwh = 8 \times V = 8 \times 80 = 640$$ cubic inches. 4. **Part b:** If only length and width are doubled, the new volume is: $$V_{new} = (2l) \times (2w) \times h = 2 \times 2 \times lwh = 4 \times V = 4 \times 80 = 320$$ cubic inches. 5. **Explanation:** Doubling all dimensions multiplies volume by $2^3 = 8$. Doubling two dimensions multiplies volume by $2^2 = 4$. **Final answers:** - a) 640 cubic inches - b) 320 cubic inches