The correct spelling is "monomials"
mono = one
nomial = name
so monomial translates to "one name"
As for the actual question of multiplying monomials, there isn't anything we can do here. The reason why is because the bases 'a' and 'v' are different. If they were both the same letter, then we'd be able to add the exponents. However that is not the case here. So we'd just leave it as a^3*v^4