$3\mathrm{.}17.$ A data cube, C$,$ has n dimensions, and each dimension has exactly p distinct values in the base

cuboid. Assume that there are no concept hierarchies associated with the dimensions.

$($a$)$ What is the maximum number of cells possible in the base cuboid?

$($b$)$ What is the minimum number of cells possible in the base cuboid?

$($c$)$ What is the maximum number of cells possible $($including both base cells and aggregate cells$)$

in the C data cube?

$($d$)$ What is the minimum number of cells possible in C$?$