Chapter 7 - Section 7.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 438: 25

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

Using the properties of radicals, then, \begin{array}{l} a^3\sqrt[]{9ab^3}-\sqrt[]{25a^7b^3}+\sqrt[]{16a^7b^3} \\= a^3\sqrt[]{9b^2\cdot ab}-\sqrt[]{25a^6b^2\cdot ab}+\sqrt[]{16a^6b^2\cdot ab} \\= a^3\cdot3b\sqrt[]{ab}-5a^3b\sqrt[]{ab}+4a^3b\sqrt[]{ab} \\= 3a^3b\sqrt[]{ab}-5a^3b\sqrt[]{ab}+4a^3b\sqrt[]{ab} \\= 2a^3b\sqrt[]{ab} .\end{array}