# Chapter R - Review Exercises - Page 76: 109

$\sqrt[12]{m}$

#### Work Step by Step

Using $\sqrt[n]{x^m}=x^{\frac{m}{n}}$ and the laws of exponents. the given expression, $\sqrt[4]{\sqrt[3]{m}} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[4]{m^{\frac{1}{3}}} \\\\= \left( m^{\frac{1}{3}} \right)^{\frac{1}{4}} \\\\= m^{\frac{1}{3}\cdot\frac{1}{4}} \\\\= m^{\frac{1}{12}} \\\\= \sqrt[12]{m^1} \\\\= \sqrt[12]{m} .\end{array}

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