What is (e^{-2x})(1/2 e^{-x}+1/2 e^{2x}) ?

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

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simplify (e^{-2x})(1/2 e^{-x}+1/2 e^{2x})

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

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

e^{- 2} \cdot e^{3}

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

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

3.7 e^{4} \cdot 5.2 e^{- 5}

20 \cdot (\frac{0.1}{3})^{- \frac{1.67 - 1}{1.67}}

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