In order to solve a negative exponent, you have to consider the multiplicative inverse of the base:
[tex]a^{-m}=\dfrac{1}{a^m}=\left(\dfrac{1}{a}\right)^m[/tex]
So, if we solve the negative exponent on the left hand side, we have
[tex]2^{-\frac{1}{2}}=\dfrac{1}{2^\frac{1}{2}}=\left(\dfrac{1}{2}\right)^{\frac{1}{2}}[/tex]
which is the right hand side.
