Why are there only words used for the numbers 2 and 3 squared and cubed?

If you take the "square" of a number, it is like drawing a square with that number as a distance. When you "cube" a number, it is like taking that distance and drawing first a square, and then a vertical square above it; a cube. We do not have any Words in English to describe 4- or 5-dimensional surfaces, so there is no special Word to describe those power functions. The number 4^4 is described as "four to the fourth power". also to describe the expression of the algebraic equation.