Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\dfrac{5a^2\sqrt[]{a}}{b^3}$
Using the properties of radicals, the given expression, $\sqrt[]{\dfrac{25a^5}{b^6}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[]{25a^5}}{\sqrt[]{b^6}} \\\\= \dfrac{\sqrt[]{25a^4\cdot a}}{\sqrt[]{b^6}} \\\\= \dfrac{\sqrt[]{(5a^2)^2\cdot a}}{\sqrt[]{(b^3)^2}} \\\\= \dfrac{5a^2\sqrt[]{a}}{b^3} \end{array} * Note that it is assumed that all variables represent positive numbers.