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

The solution to e^{-x}(2e^x+e^{2x}) is e^x+2

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

simplify

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

e^{x} + 2

Solution steps

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

Apply exponent rule:

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

= \frac{1}{e ^{x}} (2 e^{x} + e^{2 x})

Multiply fractions:

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

= \frac{1 \cdot ( 2 e ^{x} + e ^{2 x} )}{e ^{x}}

1 \cdot (2 e^{x} + e^{2 x}) = 2 e^{x} + e^{2 x}

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

Factor

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

= \frac{e ^{x} ( 2 + e ^{x} )}{e ^{x}}

Cancel the common factor:

e^{x}

= 2 + e^{x}

8.66 \cdot 1 0^{- 4}

x^{5} e^{- x^{3}} d x

e^{(- a t)} sin (wt)

e^{- 2 (l n (2))}

(e^{x - 7})^{2}