Define $A\& B$ as $A\& B = \frac{(A+B)}{2}$. What is the value of $(3\& 5) \& 8$?
I need to apply the definition of $\&$ twice, once to the inner parentheses and then to the outer one. For the inner parentheses, I have $3\& 5 = \frac{(3+5)}{2} = 4$. So I can rewrite the expression as $4\& 8$. For the outer parentheses, I have $4\& 8 = \frac{(4+8)}{2} = 6$. Therefore, the value of $(3\& 5) \& 8$ is 6.

