What is \sqrt[3]{sqrt(\sqrt[4]{2^6)}} ?

The solution to \sqrt[3]{sqrt(\sqrt[4]{2^6)}} is \sqrt[4]{2}

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simplify \sqrt[3]{sqrt(\sqrt[4]{2^6)}}

simplify

Decimal Notation

1.18920 \dots

Solution steps

Apply radical rule:

= ((2^{\frac{3}{2}})^{\frac{1}{2}})^{\frac{1}{3}}

Apply exponent rule:

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

= (2^{\frac{3}{2}})^{\frac{1}{2} \cdot \frac{1}{3}}

\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}

= (2^{\frac{3}{2}})^{\frac{1}{6}}

2^{\frac{3}{2}} = 22

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

= 2^{\frac{1}{6} + \frac{1}{12}}

Join

\frac{1}{6} + \frac{1}{12} : \frac{1}{4}

0.31 \cdot 1 0^{- 10}

(x - 1)^{3}

2.8 \cdot 1 0^{- 2} \cdot \frac{150}{1.76714}

410 e^{- 0.032 (25)}

e^{- 2 t} \cdot (- \frac{1}{2}) e^{2 t}

What is \sqrt[3]{sqrt(\sqrt[4]{2^6)}} ?
The solution to \sqrt[3]{sqrt(\sqrt[4]{2^6)}} is \sqrt[4]{2}