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

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

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

simplify

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

assuming

a \geq 0

= (ab)^{\frac{1}{4} \cdot \frac{1}{3}}

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

= (ab)^{\frac{1}{12}}

(3 ab) (2 a^{3} b)

e^{- 10.2}

500 e^{- 0.032 (10)}

x^{3} (1 - x^{2})^{3}

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