[AntonioLao]

looking through the math textbooks specially on the properties of exponents, the zero power of zero is an invalid math expression. But in order to find a connection between zero and unity, it really does not seriously violate any math logic to define that the zero power of zero is unity. it will be even more useful if the exponent is used to signify dimensionality of a number. Traditionally, real numbers are located on the one dimensional number line. And for complex numbers an imaginary axis is added perpendicular to the number line. So complex numbers are 2-dimensional numbers. Then come the 3D vector numbers extracted from the vector part of quaternions. Further generalization becomes the calculus of tensors, which are dimensional numbers greater than 3.

If exponent signifies dimension then pure scalar number must have zero dimension (rank zero tensors). Directed 1D vectors (complex numbers become rank 1 tensors) are 1 dimensional number. 2D vectors are 2 dimensional numbers becoming rank 2 tensors, 3D vectors are 3 dimensional number or rank 3 tensors, rank 4 tensors are 4D numbers, rank 5 tensors are 5D numbers, etc.