A cube has side length a. The side lengths are decreased to 20% of their original size. Write an expression in simplest form for the volume of the new cube in terms of a.

Given a cube of length, a, then when decreased by 20%, what's left is actually 80% of the original. So, for this case, we have a cube with a length of 80% (a) = 0.80a.

Now, to compute for the volume of a cube, we multiply the length three times to itself. Or, in other words, raise the length to the third power. That means the volume of the new cube is (0.8a) ³ = 0.512a³ cubic units.

Answer: 0.512a³ cubic units