# Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 18

$\dfrac{5a^2\sqrt[]{a}}{b^3}$

#### Work Step by Step

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.

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