What is \sqrt[3]{\sqrt[4]{e}} ?

The solution to \sqrt[3]{\sqrt[4]{e}} is \sqrt[12]{e}

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simplify \sqrt[3]{\sqrt[4]{e}}

simplify

Decimal Notation

1.08690 \dots

Solution steps

Apply radical rule:

= (e^{\frac{1}{4}})^{\frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= e^{\frac{1}{4} \cdot \frac{1}{3}}

\frac{1}{4} \cdot \frac{1}{3} = \frac{1}{12}

= e^{\frac{1}{12}}

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What is \sqrt[3]{\sqrt[4]{e}} ?
The solution to \sqrt[3]{\sqrt[4]{e}} is \sqrt[12]{e}