What is (\sqrt[3]{asqrt(b)})^2 ?

The solution to (\sqrt[3]{asqrt(b)})^2 is (asqrt(b))^{2/3}

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simplify (\sqrt[3]{asqrt(b)})^2

simplify

(a b)^{\frac{2}{3}}

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

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What is (\sqrt[3]{asqrt(b)})^2 ?
The solution to (\sqrt[3]{asqrt(b)})^2 is (asqrt(b))^{2/3}