Question

Show why the following statement is true: 2^−1/2 = 1/2^1/2

Answer 1

In order to solve a negative exponent, you have to consider the multiplicative inverse of the base:

$a^{-m}=\dfrac{1}{a^m}=\left(\dfrac{1}{a}\right)^m$

So, if we solve the negative exponent on the left hand side, we have

$2^{-\frac{1}{2}}=\dfrac{1}{2^\frac{1}{2}}=\left(\dfrac{1}{2}\right)^{\frac{1}{2}}$

which is the right hand side.