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

The solution to xe^{-x}*(e^{-x})/x is 1/(e^{2x)}

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simplify xe^{-x}*(e^{-x})/x

simplify

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

\frac{1}{e ^{2 x}}

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Cancel the common factor:

x

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

Multiply:

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

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

Apply exponent rule:

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

\frac{e ^{- x}}{e ^{x}} = e^{- x - x} = e^{- 2 x}

= \frac{1}{e ^{2 x}}

- 2 e^{- 2 \cdot 0}

y e^{- 2 x} (y e^{x})^{3}

(45) (45)

5.2 x 1 0^{- 10}

1.7 \cdot 1 0^{- 8} \cdot e^{0.0039 (- 27 - 20)}