How to simplify this big-O notation?

Question

I am computing the running time of an algorithm I'm analyzing. This algorithm calls $m$ times a function of running time $O(m)^{(m+3)^2}$, so we get the running time $mO(m)^{(m+3)^2}$. Can I simplify this expression? I would love to get the $m$ into the big-O-notation, but the exponent outside of the big-O throws me off. I know that $O(m)$ means there exist constants $c, m_0$ such that for all $m \geq m_0$ we have that $m \leq c*m$, but then I get stuck.