Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 77

$a^{23/12}$

Using the laws of exponents, the given expression, $ a^{2/3}\cdot a^{5/4} ,$ simplifies to \begin{array}{l}\require{cancel} a^{\frac{2}{3}+\frac{5}{4}} \\\\= a^{\frac{8}{12}+\frac{15}{12}} \\\\= a^{\frac{23}{12}} \\\\= a^{23/12} .\end{array}