Bài giải :

 ${{\left| a+7 \right|}^{2017}}+{{\left| b-3 \right|}^{2016}}=0$

Vì  $\left\{ \begin{align} & {{\left| a+7 \right|}^{2017}}\ge 0 \\ & {{\left| b-3 \right|}^{2016}}\ge 0 \\ \end{align} \right.$  nên để ${{\left| a+7 \right|}^{2017}}+{{\left| b-3 \right|}^{2016}}=0$ thì  :

$\left\{ \begin{align}& {{\left| a+7 \right|}^{2017}}=0 \\ & {{\left| b-3 \right|}^{2016}}=0 \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align}& \left| a+7 \right|=0 \\  & \left| b-3 \right|=0 \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align}& a=-7 \\  & b=3 \\ \end{align} \right.$

Khi đó $ab=-7-3=-10$.