First, we start from the GEV-distribution function:
Theorem 1.1.3 (Fisher and Tippett (1928), Gnedenko (1943)) The class of extreme value fistributions is $G_\gamma(ax+b)$ with $a>0$, $b$ real, where$$G_\gamma(x)=\exp\left(-(1+\gamma x)^{-1/\gamma}\right),\,\quad1+\gamma x>0,\quad(1.1.9)$$with $\gamma$ real and where for $\gamma=0$ the right-hand side is interpreted as $\exp(-e^{-x})$.
Then when we set gamma>0, we get the Frechet distribution, and my book says:
(a) For $\gamma>0$ clearly $G_\gamma(x)<1$ for all $x$, i.e., the right endpoint of the distribution is infinity. Moreover, as $x\to\infty$, $1-G_\gamma(x)\sim\gamma^{-1/\gamma}x^{-1/\gamma}$, i.e., the distribution has a rather heavy right tail; for example, moments of order greater than or equal to $1/\gamma$ do not exist (cf. Exercise 1.16).
But how do they come to the part of $1 - G(x) \sim\gamma^{-1/\gamma}x^{-1/\gamma}$ when $x\to\infty$?