A rectangular prism has dimensions 8 inches by 2 inches by 32 inches. If a cube has the same volume as the prism, what is the surface area of the cube, in square inches?
The cube has volume $8\cdot2\cdot32$ cubic inches, so its edge length is $\sqrt[3]{8\cdot2\cdot32}=\sqrt[3]{8\cdot64}=\sqrt[3]{8}\sqrt[3]{64}=2\cdot4=8$ inches.  The surface area of a cube with edge length 8 inches is $6(8\text{ in.})^2=\boxed{384}$ square inches.