The company is building a scale model of the theater’s main show tank for an investor's presentation. each dimension will be made 1/8    of the original dimension to accommodate the mock-up in the presentation room. what is the volume of the smaller mock-up tank?  

To represent the volume of the smaller version, you need to understand that if one dimension is 1/8 smaller, than you will apply 1/8 to each dimension in the volume.  1/8 x 1/8 x 1/8 = 1/512

This means the volume of the smaller version will be 1/512x, where x is the volume of the original.