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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

- x - \frac{1}{3} x : - \frac{4}{3} x

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

Multiply

- \frac{4}{3} x : - \frac{4 x}{3}

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

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Frequently Asked Questions (FAQ)

What is e^{-x}*e^{-1/3 x} ?
The solution to e^{-x}*e^{-1/3 x} is e^{-(4x)/3}