hi there, I'm reading a book on probability, but having trouble with following some equations. It's like this;

$\displaystyle \displaystyle \int_0^\infty \! \text{exp}\left( - \displaystyle \frac{1}{2}y^2 \right)\, dy \cdot\displaystyle \int _0^\infty \! \text{exp}\left( - \displaystyle \frac{1}{2}z^2 \right) \. dz \\ =\int_0^\infty\!\!\int_0^\infty \text{exp} \left\{- \frac{1}{2}(y^2+z^2) \right\}dydz $

I don't know how this rewriting was made; please help.

Thank you in advance.