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

Answer 1

Eva Abramson

#+- 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#

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Answer 2

Ethan Adkins

To simplify (-16)^(-1/2), first, take the square root of -16, which is imaginary, so it becomes √(-16). Then, raise it to the power of -1, which is the reciprocal, resulting in 1/√(-16). Simplify further to get 1/(4i), where i is the imaginary unit.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.