What is (e^{-2x})(1/2 e^{-2x}+1/2 e^{4x}) ?

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

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simplify (e^{-2x})(1/2 e^{-2x}+1/2 e^{4x})

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

= \frac{1 \cdot ( \frac{1}{2} e ^{- 2 x} + \frac{1}{2} e ^{4 x} )}{e ^{2 x}}

1 \cdot (\frac{1}{2} e^{- 2 x} + \frac{1}{2} e^{4 x}) = \frac{1}{2} e^{- 2 x} + \frac{1}{2} e^{4 x}

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

e^{- (\frac{π}{1 - 0.40 3 ^{2}})} \cdot 100

4.4 x 1 0^{- 9}

e^{- s t} (t - 3)

(2 yz) (2 x^{2} y z^{3})

3.2 \cdot 1 0^{- 10}

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