Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 99

$a^{6}b^{12}$

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $ \left( \sqrt[5]{a^2b^4} \right)^{15} ,$ is equivalent to \begin{array}{l}\require{cancel} (a^2b^4)^{15/5} \\\\= (a^2b^4)^{3} \\\\= a^{2(3)}b^{4(3)} \\\\= a^{6}b^{12} .\end{array}