Equality proof in Diffie-Hellman protocol?

Question

Theory

Hey!
I was digging into algorithms related to cryptography and came across the Diffie-Hellman protocol. The question arose of how this equality is proved: (g^b modp)^a≡g^ab modp
Here, the solution is given, but the last point is not very clear: math.stackexchange.com/questions/61358/prove-equiv..
Who can explain?) Thank you !

Answer 1