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}

(1.6 \cdot 1 0^{- 3}) (5 x 1 0^{0})

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

p^{1} (4, 3) y p^{2} (3, - 4)

14 m^{\circ} \frac{2}{4} m

- e^{- 0.567}