Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 95

$\sqrt[10]{m}$

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $ \sqrt{\sqrt[5]{m}} ,$ is equivalent to \begin{array}{l}\require{cancel} \left( \sqrt[5]{m} \right)^{\frac{1}{2}} \\\\= \left( m^{\frac{1}{5}} \right)^{\frac{1}{2}} \\\\= m^{\frac{1}{5}\cdot\frac{1}{2}} \\\\= m^{\frac{1}{10}} \\\\= \sqrt[10]{m^1} \\\\= \sqrt[10]{m} .\end{array}