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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

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

Cancel the common factor:

x

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

Multiply the numbers:

1 \cdot 1 = 1

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

(9.027 x 1 0^{- 5}) (3.2 x 1 0^{- 3})

a e^{- a x} \cdot a e^{- a y}

0.2 5^{- 3}

(sin^{2} (θ))^{3}