Let $a$ and $b$ be two nonzero real numbers. If the coefficient of $x ^ { 5 }$ in the expansion of $\left( a x ^ { 2 } + \frac { 70 } { 27 b x } \right) ^ { 4 }$ is equal to the coefficient of $x ^ { - 5 }$ in the expansion of $\left( a x - \frac { 1 } { b x ^ { 2 } } \right) ^ { 7 }$, then the value of $2 b$ is