Expand the Logarithmic Expression natural log of cube root of e

$\ln (\sqrt[3]{e})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{e}$ as $e^{\frac{1}{3}}$ .

$\ln (e^{\frac{1}{3}})$

Expand $\ln (e^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \ln (e)$

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

$\frac{1}{3} \cdot 1$

Multiply $\frac{1}{3}$ by $1$ .

$\frac{1}{3}$