Chapter 1 - Foundations for Algebra - 1-2 Order of Operations and Evaluating Expressions - Practice and Problem-Solving Exercises - Page 14: 42

$\dfrac{70}{9}$

Using order of operations, the given expression, $ \dfrac{2[8+(67-2^6)^3]}{9} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{2[8+(67-64)^3]}{9} \\\\= \dfrac{2[8+(3)^3]}{9} \\\\= \dfrac{2[8+27]}{9} \\\\= \dfrac{2[35]}{9} \\\\= \dfrac{70}{9} .\end{array}