The total number of boolean circuits formed will be equal to the total number of operation formed by that function.
Binary operation on set A is a function F: A x A $\rightarrow$ A.
the domain, i.e AxA has n X n elements, each of this n$ ^ {2}$ elements can be mapped to one of the elements of A.
so total $^{n^{n^{2}}}$ binary operation possible.
Hence the total boolean circuit = $^{n^{n^{2}}}$