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

The solution to \sqrt[4]{\sqrt[3]{6ab^2}} is \sqrt[12]{6}\sqrt[12]{ab^2}

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

simplify

Solution steps

Apply radical rule:

= ((6 a b^{2})^{\frac{1}{3}})^{\frac{1}{4}}

Apply exponent rule:

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

assuming

a \geq 0

= (6 a b^{2})^{\frac{1}{3} \cdot \frac{1}{4}}

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

= (6 a b^{2})^{\frac{1}{12}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

(a^{\frac{1}{4}} b^{2}) \cdot (a^{\frac{1}{4}} b^{3})

(1.4 \cdot 1 0^{1}) (8 \cdot 1 0^{4})

\frac{s ^{2}}{( s ^{2} + a ^{2} ) ^{2}}

(3 x 1 0^{5}) x (1.8 x 1 0^{- 3})

(1.8 \cdot 1 0^{1}) (7 \cdot 1 0^{5})

What is \sqrt[4]{\sqrt[3]{6ab^2}} ?
The solution to \sqrt[4]{\sqrt[3]{6ab^2}} is \sqrt[12]{6}\sqrt[12]{ab^2}