Chapter 1 - Foundations for Algebra - 1-2 Order of Operations and Evaluating Expressions - Practice and Problem-Solving Exercises - Page 14: 40

$\dfrac{55}{8}$

Using order of operations, the given expression, $ \dfrac{22+1^3+(3^4-7^2)}{2^3} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{22+1+(81-49)}{8} \\\\= \dfrac{22+1+32}{8} \\\\= \dfrac{23+32}{8} \\\\= \dfrac{55}{8} .\end{array}