Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set - Page 424: 52

$\dfrac{1}{a^{11/12}}$

Using laws of exponents, then, \begin{array}{l} \dfrac{a^{1/4}a^{-1/2}}{a^{2/3}} \\\\= a^{\frac{1}{4}+\frac{-1}{2}-\frac{2}{3}} \\\\= a^{\frac{3}{12}-\frac{6}{12}-\frac{8}{12}} \\\\= a^{-\frac{11}{12}} \\\\= \dfrac{1}{a^{11/12}} .\end{array}