A simplified expression for $\left(\sum_idx_i\otimes f_i\right)^k$

Question

Let $E\to M$ be a vector bundle over a smooth manifold. Let $\eta=\sum_idx_i\otimes f_i\in\Omega^1(X,End(E))$ be an end-valued 1-form on $M$. Is there a simplified expression for $$\eta^k=\left(\sum_idx_i\otimes f_i\right)^k?$$ In other words I am looking for endomorphisms $g_I$ such that $$\eta^k=\sum_Idx_I\otimes g_I$$ with $I=\{i_1<...<i_k\}$.