What is e^{-x^3}*(-1/3)e^{-x^3} ?

The solution to e^{-x^3}*(-1/3)e^{-x^3} is -1/3 e^{-2x^3}

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

simplify

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

- \frac{1}{3} e^{- 2 x^{3}}

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- x^{3}} e^{- x^{3}} = e^{- x^{3} - x^{3}}

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

Add similar elements:

- x^{3} - x^{3} = - 2 x^{3}

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

Remove parentheses:

(- a) = - a

= - \frac{1}{3} e^{- 2 x^{3}}

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What is e^{-x^3}*(-1/3)e^{-x^3} ?
The solution to e^{-x^3}*(-1/3)e^{-x^3} is -1/3 e^{-2x^3}