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

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

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

simplify

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

- \frac{1}{x} i

Solution steps

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

Apply exponent rule:

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

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

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

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

= \frac{1}{i ( x ^{2} ) ^{\frac{1}{2}}}

(x^{2})^{\frac{1}{2}} = x

= \frac{1}{i x}

Rewrite

i x

in standard complex form:

x i

= \frac{1}{x i}

Multiply by the conjugate

\frac{- i}{- i}

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

Simplify

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

= \frac{- i}{x}

Rewrite in standard complex form:

- \frac{1}{x} i

= - \frac{1}{x} i

e^{- \frac{12}{0.0146732}}

- \frac{2}{2} \cdot \frac{2}{2}

e^{- 0.05 \cdot 0}

e^{- t} \cdot cosh (t)

e^{- 7 π}