{|-2(-5)-38|+2}

We simplify: $\left|-2\left(-5\right)-38\right|+\frac{2}{3}\left(-9+7\right)^3=\left|2\cdot \:5-38\right|+\frac{2}{3}\left(-9+7\right)^3$, so we get $28+\frac{2}{3}\left(7-9\right)^3$ or $\boxed{\frac{68}{3}}.$

Taking what you have literally written, we have

{ |-2(-5)-38|+2} / 3 * [-9+7]^3  =

(1/3)  {   l  10 - 38  l  + 2 }  * ( -9 + 7)^3  =

(1/3)  { l - 28 l + 2 }  * (-2)^3  =

(1/3) ( 30) * (-2)^3  =

10 * ( -8)  =

-80