Why is it hard to compute $g^{xy}\bmod p$ from $g^x\bmod p$ and $g^y\bmod p$?

Question

Why is it hard to compute $$(g^x\bmod p, g^y\bmod p) \longmapsto g^{xy}\bmod p $$ when can we quickly compute $$x \longmapsto g^x\bmod p$$ ?

Answer 1

I believe you are asking a question about DH exchanging key protocol. In DH, A creates a random private key of x and then will send the mod to B.
so nobody knows the X, although everyone can see the mod they cannot get the x from it, because of DLP (Discrete Logarithm Problem).