How to show that $\prod_{d/n} d = n^{\frac{\tau(n)}{2}}$ set $ n, n \in \mathbb{N}$ and prove that 
$\prod_{d/n} d = n^{\frac{\tau(n)}{2}}$
¨I have tried this¨
If $n > 1$ then
$n = p_{1}^{\alpha_{1}}\cdot p_{2}^{\alpha_{2}}\cdots p_{k}^{\alpha_{k}}$
so 
$n^{\frac{\tau(n)}{2}}=(p_{1}^{\alpha_{1}}\cdot p_{2}^{\alpha_{2}}\cdots p_{k}^{\alpha_{k}})^{\frac{(\alpha_{1}+1)\cdot(\alpha_{2}+1)\cdots(\alpha_{k}+1)}{2}}$
but i dont know how stablish a relation with $\prod_{d/n} d$

Square the equation. On the right you get $n^{\tau(n)}$. Now try to pair the factors on the left in a good way.
