From Förberedande kurs i matematik 1

If we use \displaystyle 4=2\centerdot 2=2^{2}, the power rules give

\displaystyle 4^{-\frac{1}{2}}=\left( 2^{2} \right)^{-\frac{1}{2}}=2^{2\centerdot \left( -\frac{1}{2} \right)}=2^{-1}=\frac{1}{2}