Chapter 1, Equations and Graphs - Section 1.6 - Solving Other Types of Equations - 1.6 Exercises - Page 139: 78

$x=a^6$

$\sqrt{x}-a\sqrt[3]{x}+b\sqrt[6]{x}-ab=0$ $\sqrt[6]{x}^3-a\sqrt[6]{x}^2+b\sqrt[6]{x}-ab=0$ (Factorize) $(\sqrt[6]{x}-a)(\sqrt[6]{x}^2+b)=0$ (Note that $\sqrt[6]{x}^2+b>0$) $\sqrt[6]{x}-a=0$ $\sqrt[6]{x}=a$ $x=a^6$ Then, the solution is $x=a^6$.