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

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Answer 1 · 2016-03-28T11:52:37

$+- 1/(4i)$

Consider the example $x^(-1/2)$ . This is the same as $1/(sqrt(x))$

Now use this approach for your question.

$" "(-16)^(1/2) = 1/(sqrt(-16))$

Write $-16" as "-1xx16$ giving

$" "1/(sqrt(16)xxsqrt(-1))$

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

$" "1/(+-4)xx 1/(i)$

$" "+- 1/(4i)$

'~~~~~~~~~~~~~~~~~~~~~~~~~
If the question had been $-(16)^(-1/2)$

Then the solution would have been:

$- 1/4$

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