What is (e^{-5/3 x})(2e^{-2x}+5x) ?

The solution to (e^{-5/3 x})(2e^{-2x}+5x) is (5x+2e^{-2x}}{e^{\frac{5x)/3}}

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simplify (e^{-5/3 x})(2e^{-2x}+5x)

simplify

(e^{- \frac{5}{3} x}) (2 e^{- 2 x} + 5 x)

\frac{5 x + 2 e ^{- 2 x}}{e ^{\frac{5 x}{3}}}

Solution steps

(e^{- \frac{5}{3} x}) (2 e^{- 2 x} + 5 x)

Apply exponent rule:

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

= \frac{1}{e ^{\frac{5}{3} x}} (5 x + 2 e^{- 2 x})

\frac{1}{e ^{\frac{5}{3} x}} = \frac{1}{e ^{\frac{5 x}{3}}}

= \frac{1}{e ^{\frac{5 x}{3}}} (5 x + 2 e^{- 2 x})

Multiply fractions:

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

= \frac{1 \cdot ( 2 e ^{- 2 x} + 5 x )}{e ^{\frac{5 x}{3}}}

1 \cdot (2 e^{- 2 x} + 5 x) = 2 e^{- 2 x} + 5 x

= \frac{2 e ^{- 2 x} + 5 x}{e ^{\frac{5 x}{3}}}

(e^{\frac{y}{x}})^{2}

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

e^{- 673 (3)}

84.75 (0.08314 \cdot 288.6)^{- 2}

What is (e^{-5/3 x})(2e^{-2x}+5x) ?
The solution to (e^{-5/3 x})(2e^{-2x}+5x) is (5x+2e^{-2x}}{e^{\frac{5x)/3}}