Inequality involving exponentials and integrals

Question

I am trying to understand the following inequalities, but I am lost in the step from (1) to (2). Can't find where the $|v|^{-(p-1)/p}$ comes from. I guess I am missing some elementary inequality involving the exponential function.

Answer 1

$\left[\int_{-\pi}^{-\pi+\epsilon} e^{-vxp/(p-1)}dx\right]^{(p-1)/p}$

=$\left[ {e^{-vxp/(p-1)} \over vp/(p-1)} |_{-\pi+\epsilon}^{-\pi} \right]^{(p-1)/p}$

=$\left[{e^{v \pi p/(p-1)} - e^{v \pi p/(p-1)}e^{-v \epsilon p/(p-1)} \over vp/(p-1)} \right]^{(p-1)/p}$

That's where you get the $v^{p/(p-1)}$ term.