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

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

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simplify (e^{-1/6 x})/(e^{2/3 x)}

simplify

\frac{e ^{- \frac{1}{6} x}}{e ^{\frac{2}{3} x}}

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

Solution steps

\frac{e ^{- \frac{1}{6} x}}{e ^{\frac{2}{3} x}}

Apply exponent rule:

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

= e^{- \frac{1}{6} x - \frac{2}{3} x}

Simplify

- \frac{1}{6} x - \frac{2}{3} x : - \frac{5}{6} x

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

Multiply

- \frac{5}{6} x : - \frac{5 x}{6}

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

\frac{( 1 + x ) ^{\frac{1}{2}}}{( 1 - x ) ^{\frac{1}{2}}}

x (x^{2} + 1)^{- \frac{1}{2}}

(15 \cdot 1 0^{- 12}) (e^{\frac{0.6}{0.026}} - 1) (25)

6.0033 e^{- 0.03 x}

5 r^{2} s^{2} (2 r - 3 s)

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