Let x- = (x1, x2 ..., xn) be a vector in a space Z ⁿ with Z ring of integers and let q be a positive integer, f a polynomial in x with coefficients in Z. The exponential sum associated with f is defined as S(f;q)= ∑exp(2πif(x)/ q) where the sum is taken over a complete set of residues modulo q. The value of S(f;q) has been shown to depend on the estimate of the cardinality lVi, the number of elements contained in the set V = {xmodq I fx ? 0modq} where fx is the partial derivative of f with respect to x. To determine the cardinality of V, the information on the p-adic sizes of common zeros of the partial derivatives polynomials need to be obtained. This paper discusses a method of determining the p-adic sizes of the components of (ξ,η) a common root of partial derivatives polynomial of f(x,y) in Zp[x,y] of degree seven based on the p-adic Newton polyhedron technique associated with the polynomial. The seventh degree form considered is of the type f(x,y) = ax7 + bx ⁶y + cx ⁵y ³ + sx + ty + k.