This paper proves the uniform exponential stability of the time varying linear dynamic system $x^{\Delta}(r) = G(r)x(r)$, $r \in \mathbb{T}$ in terms of boundedness of solution of the following Cauchy problem:

$W^{\Delta}(r) = G(r)W(r) + \omega(r)$, $0 \le r \in \mathbb{T}$, $W(0) = v_0$

where $\mathbb{T}$ denotes time scale, $G(r)$ is a matrix valued function, $\omega(r)$ is a bounded function on $\mathbb{T}$ and $v_0 \in \mathbb{C}^m$. In this note we prove the results that have the above result as an immediate corollaries.