What is e^{-8x}xe^{4x}(e^{4x})/(25+x^2) ?

The solution to e^{-8x}xe^{4x}(e^{4x})/(25+x^2) is x/(x^2+25)

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simplify e^{-8x}xe^{4x}(e^{4x})/(25+x^2)

simplify

e^{- 8 x} x e^{4 x} \frac{e ^{4 x}}{25 + x ^{2}}

\frac{x}{x ^{2} + 25}

Solution steps

e^{- 8 x} x e^{4 x} \frac{e ^{4 x}}{25 + x ^{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- 8 x} e^{4 x} = e^{- 8 x + 4 x}

= x e^{- 8 x + 4 x} \frac{e ^{4 x}}{25 + x ^{2}}

Add similar elements:

- 8 x + 4 x = - 4 x

= x e^{- 4 x} \frac{e ^{4 x}}{25 + x ^{2}}

Multiply fractions:

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

= \frac{e ^{4 x} x e ^{- 4 x}}{25 + x ^{2}}

e^{4 x} x e^{- 4 x} = x

= \frac{x}{25 + x ^{2}}

e^{5} \cdot e^{- 3}

(1.67 \cdot 1 0^{- 27}) \cdot 0.016

1.95 \cdot 1 0^{- 5} k g m^{- 2} s^{- 1}

e^{- x} (e^{x} x - e^{x} + 2 x + c)

What is e^{-8x}xe^{4x}(e^{4x})/(25+x^2) ?
The solution to e^{-8x}xe^{4x}(e^{4x})/(25+x^2) is x/(x^2+25)