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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

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

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

Popular Examples

simplify e^{-7/10}simplify

e^{- \frac{7}{10}}

simplify-2.18*10^{-18}(1/(3^2)-1/(4^2))simplify

- 2.18 \cdot 1 0^{- 18} (\frac{1}{3 ^{2}} - \frac{1}{4 ^{2}})

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

simplify 500(100*10^{-6})e^{-2500(100*10^{-6})}simplify

500 (100 \cdot 1 0^{- 6}) e^{- 2500 (100 \cdot 1 0^{- 6})}

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\frac{5 - 5}{5}

Frequently Asked Questions (FAQ)

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