Show that \(A^k = \underline{Q}^{(k)}\underline{R}^{(k)}\text{,}\) where

\begin{equation*} \underline{Q}^{(k)} = Q^{(1)}Q^{(2)} \cdots Q^{(k)}, \end{equation*}

and

\begin{equation*} \underline{R}^{(k)} = R^{(k)}R^{(k-1)} \cdots R^{(1)}. \end{equation*}