Meaning of equations involving modular arithmetic

Question

Does the following congruence equations have any meaning? If yes then please elaborate on what is it in a simplified form?

For integers a,b,c,p,m,n...

a ≡ b mod(m) mod(n)

p ≡ c^(mod(a))

p ≡ c^(mod(a)) mod(b)

Answer 1

The second and third equations make no sense. The first would make sense in form: $$a\equiv ((b \mod m) \mod n)$$