Expand the Logarithmic Expression natural log of fifth root of e

$\ln (\sqrt[5]{e})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{e}$ as $e^{\frac{1}{5}}$ .

$\ln (e^{\frac{1}{5}})$

Expand $\ln (e^{\frac{1}{5}})$ by moving $\frac{1}{5}$ outside the logarithm.

$\frac{1}{5} \ln (e)$

The natural logarithm of $e$ is $1$ .

$\frac{1}{5} \cdot 1$

Multiply $\frac{1}{5}$ by $1$ .

$\frac{1}{5}$