Abstract: Let P be arbitrary a point inside the simplex A in the n-dimensional Eucidean space Eⁿ . Let d be the distance from the point P to the correspondent hyperplane of vertex A_i of A.Let r denote the inradius of A. In this paper,we obtain a very strong negative eaponent geometric inequatity of contact with d₁,d₂,...,d_n+1 and r.

Key words:  , negative exponent geometric inequality, simplex, inradius