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#