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Popular >

simplify e^{x/3}e^{-(5x)/6}

Solution

simplify

e^{\frac{x}{3}} e^{- \frac{5 x}{6}}

Solution

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

Solution steps

e^{\frac{x}{3}} e^{- \frac{5 x}{6}}

Apply exponent rule:

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

= e^{\frac{x}{3}} \frac{1}{e ^{\frac{5 x}{6}}}

Multiply fractions:

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

= \frac{1 \cdot e ^{\frac{x}{3}}}{e ^{\frac{5 x}{6}}}

Multiply:

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

= \frac{e ^{\frac{x}{3}}}{e ^{\frac{5 x}{6}}}

Apply exponent rule:

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

\frac{e ^{\frac{x}{3}}}{e ^{\frac{5 x}{6}}} = e^{\frac{x}{3} - \frac{5 x}{6}} = e^{- \frac{x}{2}}

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

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Frequently Asked Questions (FAQ)

What is e^{x/3}e^{-(5x)/6} ?
The solution to e^{x/3}e^{-(5x)/6} is 1/(e^{x/2)}