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

The solution to \sqrt[3]{sqrt(2\sqrt[3]{4)}} is 2^{5/18}

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

simplify

2^{\frac{5}{18}}

Decimal Notation

1.21232 \dots

Solution steps

Apply radical rule:

Apply exponent rule:

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

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

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}{9}}

Join

\frac{1}{6} + \frac{1}{9} : \frac{5}{18}

= 2^{\frac{5}{18}}

6 (1.66022 \cdot 1 0^{- 19})

3 x (16 x^{2})

\frac{d}{d t} ((f (t, y)) (y e^{- a t}))

\frac{Δ ^{15.4}}{Δ ^{3}}

(1.6 \cdot 1 0^{- 19}) \cdot 700

What is \sqrt[3]{sqrt(2\sqrt[3]{4)}} ?
The solution to \sqrt[3]{sqrt(2\sqrt[3]{4)}} is 2^{5/18}