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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

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

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

Apply exponent rule:

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

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

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

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Frequently Asked Questions (FAQ)

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