What is simplify-(2e^{-2x}-e^{-x})(1/3 e^{-4x}) ?

The solution to simplify-(2e^{-2x}-e^{-x})(1/3 e^{-4x}) is -(-e^x+2)/(3e^{6x)}

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simplify-(2e^{-2x}-e^{-x})(1/3 e^{-4x})

simplify

- (2 e^{- 2 x} - e^{- x}) (\frac{1}{3} e^{- 4 x})

- \frac{- e ^{x} + 2}{3 e ^{6 x}}

Solution steps

- (2 e^{- 2 x} - e^{- x}) (\frac{1}{3} e^{- 4 x})

Apply exponent rule:

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

= - \frac{1}{3} \cdot \frac{1}{e ^{4 x}} (2 e^{- 2 x} - e^{- x})

Multiply fractions:

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

= - \frac{1 \cdot 1 \cdot ( 2 e ^{- 2 x} - e ^{- x} )}{3 e ^{4 x}}

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

= - \frac{2 e ^{- 2 x} - e ^{- x}}{3 e ^{4 x}}

Cancel

\frac{2 e ^{- 2 x} - e ^{- x}}{3 e ^{4 x}} : \frac{- e ^{x} + 2}{3 e ^{6 x}}

= - \frac{- e ^{x} + 2}{3 e ^{6 x}}

3 (1 + x)^{- 1}

e^{- 2 j x}

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

(x^{4} y^{3}) (x^{4} y)

(2.8 \times 1 0^{- 4}) (5)^{1.08}

What is simplify-(2e^{-2x}-e^{-x})(1/3 e^{-4x}) ?
The solution to simplify-(2e^{-2x}-e^{-x})(1/3 e^{-4x}) is -(-e^x+2)/(3e^{6x)}