What is \sqrt[3]{\sqrt[4]{21}} ?

The solution to \sqrt[3]{\sqrt[4]{21}} is \sqrt[12]{21}

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simplify \sqrt[3]{\sqrt[4]{21}}

simplify

3421

1221

Decimal

1.28879 \dots

Solution steps

3421

Apply radical rule:

n a = a^{\frac{1}{n}}

= (2 1^{\frac{1}{4}})^{\frac{1}{3}}

Apply exponent rule:

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

= 2 1^{\frac{1}{4} \cdot \frac{1}{3}}

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

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

a^{\frac{1}{n}} = n a

= 1221

\frac{d}{d x} ((x + y^{2})^{4})

\frac{1}{1.097 \cdot 1 0 ^{7}} (\frac{1}{16} - \frac{1}{25})^{- 1}

b^{\frac{5}{2}} c^{\frac{5}{11}} (b^{\frac{3}{2}} c^{\frac{7}{11}})

(6.6 \cdot 1 0^{- 34}) (3 \cdot 1 0^{8})

(2 a^{2} b) (4 a b^{2} c)

What is \sqrt[3]{\sqrt[4]{21}} ?
The solution to \sqrt[3]{\sqrt[4]{21}} is \sqrt[12]{21}