I am trying to understand the proof of the mean value formula for Laplace's equation in Partial Differential Equations by Evans: If $u \space \epsilon \space C^2(U)$ is harmonic, then 
(16) is equivalent to $$ u(x) = \frac{1}{n\alpha(n) r^{n-1}}\int_{\partial B(x,r)} udS = \frac{1}{\alpha(n) r^{n}}\int_{B(x,r)} udS$$
Here, $\alpha(n)$ is the volume of the unit ball in $ \Bbb{R}^n$.
He starts the proof with this line:
I am confused about the second equality in this statement. I can see he is using the transformation $ y = x + rz$ but the Jacobian of this transformation should be $r^n$ and then that would get you $$\frac{1}{n\alpha(n) r^{n-1}}\int_{\partial B(x,r)} u(y)dS = \frac{1}{n\alpha(n) r^{n-1}}\int_{\partial B(x,r)} u(x+rz) r^ndS = \frac{r}{n\alpha(n)}\int_{\partial B(x,r)} u(x+rz)dS $$
According to the proof as laid out in the book, that final $r$ outside the integral should cancel out somehow but I'm not sure how. Can someone elaborate how that equality works out? Any help would be appreciated.