What is (\sqrt[5]{81ab^3})^3 ?

The solution to (\sqrt[5]{81ab^3})^3 is 81^{3/5}(ab^3)^{3/5}

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simplify (\sqrt[5]{81ab^3})^3

simplify

8 1^{\frac{3}{5}} (a b^{3})^{\frac{3}{5}}

Solution steps

Apply radical rule:

= ((81 a b^{3})^{\frac{1}{5}})^{3}

Apply exponent rule:

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

= (81 a b^{3})^{\frac{1}{5} \cdot 3}

\frac{1}{5} \cdot 3 = \frac{3}{5}

= (81 a b^{3})^{\frac{3}{5}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 8 1^{\frac{3}{5}} (a b^{3})^{\frac{3}{5}}

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What is (\sqrt[5]{81ab^3})^3 ?
The solution to (\sqrt[5]{81ab^3})^3 is 81^{3/5}(ab^3)^{3/5}