But Coulomb's Constant is: 1/4 pi Epsilon0

and Ampere's Constant is: Mu0/4 pi

Why is it that these "correcting factors" (Epsilon0 and Mu0) were introduced in the denominator in one constant, and in the numerator in the other constant? For example, they could have just made Ampere's Constant 1/4 pi Mu0, in order to resemble Ampere's Constant. Considering the values of Epsilon0 and Mu0 are

*defined*, they were free to put them wherever they wanted. They could have just said Epsilon0 was 8.8 x 10^12, as opposed to 8.8 x 10^-12 and written Coulomb's Constant as Epsilon0/4 pi, in order to resemble Ampere's Constant.

So, what gives?