# How do you simplify (-16)^(-1/2) ?

Mar 28, 2016

$\pm \frac{1}{4 i}$

#### Explanation:

Consider the example ${x}^{- \frac{1}{2}}$. This is the same as $\frac{1}{\sqrt{x}}$

Now use this approach for your question.

$\text{ } {\left(- 16\right)}^{\frac{1}{2}} = \frac{1}{\sqrt{- 16}}$

Write $- 16 \text{ as } - 1 \times 16$ giving

$\text{ } \frac{1}{\sqrt{16} \times \sqrt{- 1}}$

The square root of negative 1 gives rise to the complex number context. So we have:

$\text{ } \frac{1}{\pm 4} \times \frac{1}{i}$

$\text{ } \pm \frac{1}{4 i}$

'~~~~~~~~~~~~~~~~~~~~~~~~~
If the question had been $- {\left(16\right)}^{- \frac{1}{2}}$

Then the solution would have been:

$- \frac{1}{4}$