What is (-e^{-x})^{-1} ?

The solution to (-e^{-x})^{-1} is -e^x

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

simplify

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

- e^{x}

Solution steps

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

Apply exponent rule:

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

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

Apply the fraction rule:

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

= - \frac{1}{e ^{- x}}

Apply exponent rule:

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

e^{- x} = \frac{1}{e ^{x}}

= - \frac{1}{\frac{1}{e ^{x}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

\frac{1}{\frac{1}{e ^{x}}} = \frac{e ^{x}}{1}

= - \frac{e ^{x}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{e ^{x}}{1} = e^{x}

= - e^{x}

4000 (1.1)^{- 4}

2.05 \cdot 1 0^{- 2}

0.64

(x y) (x y^{2})

a^{3} b^{3} c^{3}