Can you please help?

Problem. An exponential distribution is a member of the Gamma Family; that is, when $\displaystyle \alpha = 1$, the pdf reduces to the exponential distribution (with $\displaystyle \lambda = 1/\beta$). Let the r.v. $\displaystyle X ~$ Exponential$\displaystyle (\beta)$, then $\displaystyle Y = X^\frac{1}{\gamma}, \gamma>0$, has a Weibull $\displaystyle (\gamma, \beta)$ distribution. Show the density function of $\displaystyle Y$ is

$\displaystyle f_Y(y|\gamma, \beta) = \frac{\gamma}{\beta}y^{\gamma-1} e^\frac{-y^\gamma}{\beta}$.

I have in my notes that for X~Exponential, $\displaystyle f_X(x) = \lambda e^{-\lambda x}$.

Thanks!