Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 72

$8^{9/11}$

Using the laws of exponents, the given expression, $ \dfrac{8^{7/11}}{8^{-2/11}} ,$ simplifies to \begin{array}{l}\require{cancel} 8^{\frac{7}{11}-\left( -\frac{2}{11} \right)} \\\\= 8^{\frac{7}{11}+\frac{2}{11}} \\\\= 8^{\frac{9}{11}} \\\\= 8^{9/11} .\end{array}