What is (\sqrt[112]{a^2b^3})^8 ?

The solution to (\sqrt[112]{a^2b^3})^8 is \sqrt[14]{a^2b^3}

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simplify (\sqrt[112]{a^2b^3})^8

simplify

Solution steps

Apply radical rule:

= ((a^{2} b^{3})^{\frac{1}{112}})^{8}

Apply exponent rule:

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

= (a^{2} b^{3})^{\frac{1}{112} \cdot 8}

\frac{1}{112} \cdot 8 = \frac{1}{14}

= (a^{2} b^{3})^{\frac{1}{14}}

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What is (\sqrt[112]{a^2b^3})^8 ?
The solution to (\sqrt[112]{a^2b^3})^8 is \sqrt[14]{a^2b^3}