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

The solution to e^{-2x}((e^{-2x})/(x^2)) is 1/(e^{4x)x^2}

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

simplify

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

\frac{1}{e ^{4 x} x ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

1 \cdot e^{- 2 x} = e^{- 2 x}

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

Apply exponent rule:

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

\frac{e ^{- 2 x}}{e ^{2 x}} = e^{- 2 x - 2 x} = e^{- 4 x}

= \frac{1}{e ^{4 x} x ^{2}}

(- \frac{1}{2} e^{2 x} + \frac{1}{6} e^{3 x}) (\frac{1}{3} e^{- 4 x})

e^{- 0.0001216}

50 e^{- 0.223 \cdot 3}

e^{- a t} sin (ω t u)

b^{2} \cdot 4 a^{2}

What is e^{-2x}((e^{-2x})/(x^2)) ?
The solution to e^{-2x}((e^{-2x})/(x^2)) is 1/(e^{4x)x^2}