Getting closer to the powers of $e$ !

Let $g:\mathbb{R}\to\mathbb{R}$ be a differentiable function such that $g(2)=-40$ and $g^{\prime}(2)=-5$ . Then find the value of $\displaystyle \lim _{ x\to 0 }{ { \left( \dfrac { g\left( 2-{ x }^{ 2 } \right) }{ g\left( 2 \right) } \right) }^{\frac { 4 }{ { x }^{ 2 } } } }$ .

Notation:

• $g^{\prime}(x)$ denotes the first derivative of $g(x)$ .
• $e \approx 2.718$ is the Euler's number .