What is (-16)^{-1/2} ?

The solution to (-16)^{-1/2} is -1/4 i

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simplify (-16)^{-1/2}

simplify

(- 16)^{- \frac{1}{2}}

- \frac{1}{4} i

Solution steps

(- 16)^{- \frac{1}{2}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(- 16)^{- \frac{1}{2}} = \frac{1}{( - 16 ) ^{\frac{1}{2}}}

= \frac{1}{( - 16 ) ^{\frac{1}{2}}}

(- 16)^{\frac{1}{2}} = 1 6^{\frac{1}{2}} i

= \frac{1}{1 6 ^{\frac{1}{2}} i}

1 6^{\frac{1}{2}} = 4

= \frac{1}{4 i}

Multiply by the conjugate

\frac{- i}{- i}

= \frac{1 \cdot ( - i )}{4 i ( - i )}

Simplify

\frac{1 \cdot ( - i )}{4 i ( - i )} : \frac{- i}{4}

= \frac{- i}{4}

Rewrite in standard complex form:

- \frac{1}{4} i

= - \frac{1}{4} i

e^{- 2 x} (1 - 2 x)

x^{\frac{3}{2}} \cdot x

(e^{x})^{y}

(e^{x})^{x}

2.3 \times 1 0^{- 5}