What is sqrt(\sqrt{\sqrt[3]{8e^{24)}}} ?

The solution to sqrt(\sqrt{\sqrt[3]{8e^{24)}}} is \sqrt[4]{2}e^2

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simplify sqrt(\sqrt{\sqrt[3]{8e^{24)}}}

simplify

Decimal Notation

8.78711 \dots

Solution steps

Apply radical rule:

= ((8 e^{24})^{\frac{1}{6}})^{\frac{1}{2}}

Apply exponent rule:

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

= (8 e^{24})^{\frac{1}{6} \cdot \frac{1}{2}}

\frac{1}{6} \cdot \frac{1}{2} = \frac{1}{12}

= (8 e^{24})^{\frac{1}{12}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply exponent rule:

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

e^{24} = e^{2 \cdot 12} = (e^{2})^{12}

Apply radical rule:

assuming

a \geq 0

500 e^{- 0.0244 (30)}

- 3 e^{- 3 (0)}

e^{- 0. 5^{2}}

x^{- 1} d x

e^{2} \cdot e^{- 2}

What is sqrt(\sqrt{\sqrt[3]{8e^{24)}}} ?
The solution to sqrt(\sqrt{\sqrt[3]{8e^{24)}}} is \sqrt[4]{2}e^2